Novel dual-loop bi-evaporator vapor compression refrigeration cycles for freezing and air-conditioning applications

Accepted Manuscript Research Paper Novel dual-loop bi-evaporator vapor compression refrigeration cycles for freezing and air-conditioning applications Hadi Rostamzadeh, Javad Rostamzadeh, Pouria Seyed Matin, Hadi Ghaebi PII: DOI: Reference:

S1359-4311(18)30690-2 https://doi.org/10.1016/j.applthermaleng.2018.04.085 ATE 12082

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

31 January 2018 14 April 2018 16 April 2018

Please cite this article as: H. Rostamzadeh, J. Rostamzadeh, P. Seyed Matin, H. Ghaebi, Novel dual-loop bievaporator vapor compression refrigeration cycles for freezing and air-conditioning applications, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.04.085

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Novel dual-loop bi-evaporator vapor compression refrigeration cycles for freezing and air-conditioning applications

Hadi Rostamzadeh1,a,d, Javad Rostamzadehb, Pouria Seyed Matinc, Hadi Ghaebid a

Department of Aerospace Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran b

Department of Mechanical Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran

c

d

Department of Mechanical Engineering, Faculty of Aerospace Engineering, Tarbiat Modares University, Tehran, Iran

Department of Mechanical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, P.O.Box 179, Ardabil, Iran

Abstract Cooling production at different temperature levels for various applications has been highlighted in recent years since the produced cooling capacity must be used for different applications to meet all subjects’ demands. For this purpose, a novel dual-loop bi-evaporator vapor compression refrigeration cycle is proposed to meet these demands for freezing and air-conditioning applications which can be employed in building sectors. Later, ejector expander is used in place of the expansion valve in the proposed refrigeration system to enhance the performance of this basic system based on the thermodynamics and thermoeconomics viewpoints. Four working fluids of R717, R290, R600a, and R134a are examined where R717 is recommended from thermodynamics, thermoeconomics, and environment viewpoints. The results indicated that using ejector expander in place of the

1

Corresponding Author: Email Addresses: [email protected] or [email protected] Tel.: +98 933 8084807

expansion valve and R717 as working fluid, the freezing capacity, air-conditioning capacity, coefficient of performance (COP), exergy efficiency, and sum unit cost of cooling can be increased 10.09%, 1.93%, 22.35%, 57.97%, and 11.03%, respectively. Also, the results indicated that among all components, compressors and evaporators account for the highest exergy destruction rate and investment cost. At last, a comprehensive parametric study is conducted in order to understand the performance characteristics of the proposed refrigeration systems. It is demonstrated that a higher COP and exergy efficiency can be obtained at lower condenser temperatures or higher evaporators temperatures.

Keywords: Bi-evaporator, Vapor compression refrigeration cycle (VCRC), Throttling loss, Ejector expander, Thermodynamic analysis, Thermoeconomic analysis; Nomenclature

Symbols

Subscripts and superscripts

A

area (

B

c

cost per exergy unit (

)

cost rate (

)

)

CI

basic capital investment

com

compressor

COP

Coefficient of performance

cond

condenser

CR

Compression ratio

CV

control volume

CRF

capital recovery factor

D

destruction

EERC

Ejector expander refrigeration cycle

d

diffuser

ERC

Ejector refrigeration cycle

eva

evaporator

E.V

expansion valve

EE

Ejector expander

h

specific enthalpy

ej

ejector

ID

Exergy destruction rate (kW)

ev

expansion valve

ir

interest rate

ex

exergy

m

mixer

F

fuel

mass flow rate

i

ith component

annual number of hours (h)

im

improvement

N

n

nozzle

in

inlet

nr

componets expected life

is

isentropic

n

molar flow rate

L

loss

P

pressure

LMTD

logarithmic

mean

temperature difference pf

primary flow

m

mixer

heat transfer rate

n

nozzle

R

reference

OM

operating & maintenance

s

specific entropy

out

outlet

S gen

Entropy generation rate (kW/K)

P

product

sf

secondary flow

pf

primary flow

SUCP

sum unit cost of the product

PH

physical

T

temperature

pum

pump

U

overall

heat

( u

velocity (

v

transfer

coefficient Q

heating

) s

constant entropy

specific volume

sep

separator

VCRC

Vapor compression refrigeration cycle

sf

secondary flow

YD

Exergy destruction ratio (%)

suc

suction

Z

investment cost of components ($)

tot

total value

vg

Vapor generator

w

water

W

work

)

investment cost rate of components (

Greek Symbols

)

??

efficiency (%)

μ

mass entrainment ratio

1, 2, …

cycle locations

ϕ

maintenance factor

0

dead state

ψ

exergy rate

Power (kW)

1. Introduction Refrigeration technologies have key role in human's daily life, industrial activities, welfare appliances, bio-technologies, and economic developments of countries. Over decades, a great

deal of efforts has been accomplished to use the ubiquitous resources of renewable energies or mechanical power in the refrigeration systems more efficiently from thermodynamics, economics as well as environmental impacts points of views. Many researches on refrigeration systems have been done in order to modify and make these technologies more efficient and economic along with more environmentally friendly. Nowadays, cooling production for various applications has been highlighted since the produced cooling must be set for different subjects like food or different sections of the industry. With this regard, multi-evaporator refrigeration systems are introduced due to their high capacity and wide range of usability for practical applications. Many investigators employed this concept in different refrigeration systems, such as vapour compression refrigeration cycle (VCRC), absorption refrigeration cycle (ARC), ejector refrigeration cycle (ERC), etc. [1]. For example, Sarkar [2] presented two novel multi-evaporator trascritical CO2 refrigeration systems, using constant pressure mixing model inside the ejector. They showed that the performance of single-evaporator system will be increased with the increase in the cooling capacity ratio of high-temperature evaporator to low-temperature evaporator. More recently, Sarkar [3] presented four different triple-evaporator two-stage compression refrigeration systems (EECRSs) for three different applications of refrigeration (-20 ), airconditioning (5 ) and freezing (-40 ). Thermodynamic analysis revealed that the proposed systems have 20% higher coefficient of performance (COP) compared to the basic expansion valve two-stage compression, 67% compared to the single-stage ejector compression cycle, and 117% compared to the basic expansion valve single-stage compression system. Lontsi et al. [4] proposed and analyzed a combined compression/ejection refrigeration cycle for refrigeration and freezing production purposes, using different environmentally friendly working fluids. They concluded that an increase in the evaporation temperature decreases the COP of system, while an increase in the freezing temperature increases the COP of system.

Yan et al. [5] used zeotropic mixture of R290/R600a in a modified vapour-compression refrigeration cycle (MVCRC) for domestic applications of refrigeration and freezing and compared their results with those of the traditional VCRC (TVCRC). They found that the MVCRC gives the most excellent performances in the COP, volumetric refrigeration capacity, exergy efficiency, and total exergy destruction rate under the same given operating conditions. In addition to the cited theoretical analysis, experimental analysis of multievaporator refrigeration cycles is also taken into consideration in recent years. For instance, Zheng and Deng [6] conducted an experimental investigation on the use of two-stage evaporator in the transcritical CO2 ejector expansion refrigeration system under variable operating conditions. They showed that the evaporator plays a significant role in improving the system performance which is more pronounced at lower ejector entrainment ratios. Li et al. [7] developed an experimental study on a multi-evaporator refrigeration system (MERS) with conventional pressure regulating valve and variable ejector area ratio. They demonstrated that the energy efficiency of the MERS can be improved by 12% when the conventional pressure regulating valve is replaced by a variable ejector area ratio. Vapor compression refrigeration cycle is the most frequently used refrigeration cycle which consists of a compressor, a condenser, an evaporator, an expansion device and some connector components like tubes. Due to the widespread usages of VCRC, numerous energy and exergy analysis have been done to investigate performance characteristics of the VCRC more coherently. The second law analysis of the VCRC was pioneered by Yumrutas et al.[8] in 2002. They found that the evaporator and condenser temperatures have strong effects on the exergy losses in the evaporator and condenser and on the exergy efficiency but little effects on the exergy losses in the compressor and expansion valve. Later, Ahamed et al.[9] corroborated the results of this group and added that the R134a presents the highest performance from the second law of thermodynamics viewpoint. They also demonstrated that

the compressor had the major part of exergy losses which can be reduced by the use of nanofluid and nanolubricant. Also, Arora and Kaushik[10] recommended R507a as a suitable substitute to R502 than R404a. In a similar study carried out by Kabul et al.[11], exergy analysis of VCRC with an internal heat exchanger (IHE) is performed, using R600a as an alternative solution for engineers. They confirmed the results of the previous studies and introduced compressor and IHE as the most irreversible components, respectively. However, Bayrakci and Ozgur[12] reported higher COP and exergy efficiency values with R1270 and R600 than R600a and R290. Anand and Tyagi [13] conducted an experimental analysis on VCRC using different percentage of refrigerant charge based on the second law of thermodynamics. Their results indicated that compressor and condenser are accountable for the highest and lowest losses in the VCRC, respectively. In addition, they made a conclusion that the total exergy destruction is highest when the system is 100% charged, whereas is least when the system is 25% charged. Reddy et al. [14] analyzed performance of the VCRC based on the second law of thermodynamics, using different conventional working fluids. They concluded that R134a is the best working fluid from all aspects, while R407c is the worst one. They also discussed on effects of different critical parameters such as sub-cooling of condenser outlet, superheating of evaporator outlet and effectiveness of vapor liquid heat exchanger on the performance of the system. More recently, Ma et al. [15] presented analytical expression to compute the COP of VCRC without recourse to thermodynamic diagrams or equations of state. They also presented a global entropy generation analysis for evaluating the impact of interacted processes on the COP. Srinivasan et al. [16] presented exergy charts for carbon dioxide based on the new fundamental equation of state and implemented this concept in full thermodynamic analysis of conventional and transcritical VCRCs. They reported some correlations for calculation of the exergy efficiency and COP which were valid in specific ranges. Joybari et al. [17] carried out experimental investigation

on performance evaluation of a domestic VCRC, using Taguchi method. They also optimized the performance of system showing that the amount of charge required for R600a was 66% lower than R134a at the optimum condition which significantly reduces the risk of flammability of the hydrocarbon refrigerant along with the cost of operation. Sayyaadi and Nejatolahi [18] optimized performance of the VCRC assisted with a cooling tower by considering two performance criteria, namely, total exergy destruction and total product cost of system. They considered single- and multi-objective optimization methods and demonstrated that the multi-objective optimal design more acceptably satisfies generalized engineering criteria than single-objective optimal design. Yataganbaba et al. [19] conducted thermodynamic analysis (i.e., energy and exergy analysis) of a bi-evaporator VCRC, using three different working fluids of R1234yf, R1234ze, and R134a. They showed that the greater and lower portions of exergy destruction take place in compressor and mixing chamber, respectively. They also recommended R1234ze and R134a as the appropriate working fluids for the proposed system due to their high exergy efficiency. Meanwhile, in recent decades, ejector has been used in industry in numerous ways, even singly or in stages to create a wide range of vacuum conditions. A simple and common used ejector can provide following advantages over the conventional pre-used equipment such as pump [20]: 

Rugged and simple construction.



Simple operation.



Requires no mechanical power.



Less maintenance requirements.



Capability of handling enormous volumes of gases in relatively small sizes of equipment.

A simple single-stage ejector comprises of an actuating nozzle, suction chamber and a diffuser. The main purpose is to compress and transport a weight of induced fluid from the suction pressure to the exit pressure which can be carried out by employing multistage ejectors [1]. This will reduce the size and steam consumption of the succeeding stages [1]. With this regard, Ebadollahi et al. [21] evaluated performance of an ejector refrigeration cycle using multi-parallel ejectors with seven different working fluids. From energy and exergy prospects, their results showed that the maximum coefficient of performance (COP) can be obtained 0.344 for when R152a is used as working fluid. Ejectors can be used either as a thermal compressor [22, 23] or as an expander [24, 25] in order to reduce losses through the system. The main issue in the ejector expander is generating of a pressure rise in the diffuser for minimum compressor work and optimum COP improvement [26, 27]. With this respect, Rostamzadeh et al. [28] used ejector expanders in place of throttling valves of a conventional trigeneration system, showing that the thermal and exergy efficiencies can be improved up to 6.59% and 29.33%, respectively. Sag et al. [24] used ejector as an expander in place of throttling valve in a VCRC, theoretically and experimentally. In their study, R134a is used as the most appropriate working fluid for achieving energy recovery and decreasing the irreversibility effects. It is demonstrated that the COP and exergy efficiency of the ejector expander VCRC (EEVCRC) are 7.34-12.87 % and 6.6-11.24 % higher than those in the basic VCRC (BVCRC), respectively. Ersoy and Bilir [29] investigated the effects of ejector components efficiencies on performance of an ejector expander refrigeration cycle, showing that as the ejector components efficiencies increase, the COP and exergy efficiency will increase. They also made a conclusion that as the ejector components efficiencies fall, the optimum ejector area ratio increases. In another

study carried out by this group [30], the effects of key parameters including gas cooler outlet pressure, gas cooler outlet temperature, evaporator temperature, and suction nozzle pressure drop on the main performance criteria of the basic and ejector expander CO 2 refrigeration cycles including COP, ejector area ratio, and exergy efficiency were investigated. They showed that the suction nozzle’s pressure drop has a significant effect on the ejector area ratio, COP and exergy efficiency. They also demonstrated that use of ejector as an expander always has higher COP and exergy efficiency than conventional (basic) cycle under any operation conditions since the total irreversibility of system is decreased through this replacement. Later, this group conducted similar experimental study and showed that although the drop in the refrigerant pressure in the evaporator of the ejector expander system was almost negligible, it rose as high as 133 kPa in the basic system [31]. These findings were also consistent with those of Li et al. [32], conducting a similar investigation on an ejector expander refrigeration cycle (EERC). However, they also found that the COP and volumetric cooling capacity (VCC) of EERC can be peak up to 5.91 and 2590.76 kJ/m3, respectively. On the other hand, use of ejector as a thermal compressor is also highlighted in recent decades. For example, Li et al. [33] used ejector in the organic Rankine cycle (ORC) to decrease the turbine backpressure and increase the pressure difference through it, which resulted in an increase of the output power capacity. For this purpose, they employed a second-stage evaporator worked as the primary flow of the ejector. In a similar study, Kheiri et al. [34] used ejector in ORC to improve the thermal efficiency along with the net power with various working fluids. They proposed four new ORCs with different arrangements of ejector. They demonstrated that the thermal efficiency of the basic ORC can be improved by 13.21%, 15.3%, 18.35% and 19.29% for the cases (I-VI), respectively. The same idea in the use of ejector can be taken into consideration in other power plants such as Kalina cycle

(KC), absorption power cycle (APC), etc. With the respect, Li et al. [35] used ejector in KC to decrease the exhaust pressure of the expander by the ejector, resulting in the increase of working pressure difference of the expander. As a result of this replacement, they showed that the output power and thermal efficiency of the system are increased compared to the basic KC. Saleh [36] presented a comprehensive working fluid screening for the ERC, using constant-pressure mixing model inside the ejector. His results showed that R245ca is the best selection among all candidates, however, its environment and safety aspects must be paid more attention. Smierciew et al. [37] presented an experimental investigation on the ERC for air-conditioning applications, using isobutane as working fluid at motive vapor temperature below 75 . The results of this study demonstrated that ERC can be competitive with ARC for motive heat source lower than 80 . Analyzing a system from energy and exergy viewpoints are not enough for academic and industrial applications which deal with economic issues. Thus, thermoeconomic (or exergoeconomic) study is necessary to be carried out to materialize the manufacturing process of the designed system. Thermoeconomics concept was developed by Tsatsaronis [38] in which he optimized performance of a thermal system by adding cost of system as new objective function to previous objectives (i.e., thermal efficiency and irreversibility). Many thermoeconomic studies on thermal systems such as refrigeration systems, heat exchangers, and power plants have been accomplished by researches to design and evaluate the performance of systems thereafter. Al-Otaibi et al. [39] studied the first law of thermodynamic in addition to the cost terms in a vapor compression refrigeration system. They used R134a as working fluid and specified cost parameters incorporated to each components of system. Selbaş et al. [40] presented exergoeconomic optimization of subcooled and superheated vapor compression refrigeration cycle with three different working fluids of R22, R134a, and R407c. They reported an optimum heat exchanger area

with the corresponding optimum subcooling and superheating temperatures. On the other hand, exergoeconomic analysis of ejector refrigeration cycle powered by internal combustion engine conducted by Sadeghi et al. [41], illustrating that the operating state of ERC can be optimized based on the exergy efficiency and unit cost of the product when generator, condenser and evaporator temperatures are set into 95.54 , 33.44 , and 0.03 , respectively. Calise[42] presented thermoeconomic analysis and optimization of a solardriven heating and cooling system for different types of school buildings and Italian climates. They found that the proposed system can be economically profitable only in case of public funding policies. As discussed in the reviewed literatures, different applications of VCRC in domestic or industrial markets are taken into account due to its simple structure, convenient installation, economical and comfortable setup, etc. [9, 39]. However, no comprehensive investigation on employing dual-loop bi-evaporator VCRC is carried out up to yet. Nevertheless, in some cases producing refrigeration at different temperature levels with high efficiency and low product cost (compared to the basic system) can be more applicable. This can be addressed by presenting dual-loop bi-evaporator refrigeration cycle based on VCRC. At dual-loop bievaporator systems, each loop works at specific pressure level, where each pressure level is compressed to a common pressure (here condenser pressure) with different compression ratios (CRs). To the best of the authors’ knowledge and by surveying similar literature reviews, thermodynamic modeling of dual-loop bi-evaporator VCRC system (called DB-VCRC hereafter) in the present form is not performed up to yet. In this study, a comprehensive investigation on DB-VCRC system is conducted based on the thermodynamics and thermoeconomics viewpoints. In addition, ejector expanders are employed in place of

throttling valves in basic the DB-VCRC (BDB-VCRC) system to improve its performance. The main purposes of the present study are multi-fold and can be summarized as follows:

 To propose a novel basic dual-loop bi-evaporator vapor compression refrigeration cycle.

 To enhance performance of the proposed system by employing ejector expanders in place of expansion valves.

 To analyze the proposed cycles from thermodynamics and thermoeconomics viewpoints.

 To study the effect of some key parameters on the main performance criteria. 2. System description Schematics of the proposed novel BDB-VCRC and ejector expander DB-VCRC (EEDBVCRC) systems with their corresponding T-s diagrams are shown in Figs. 1 and 2, respectively. The main components of BDB-VCRC system are as follows: two compressors, two evaporators, two expansion valves and a condenser (Fig. 1). The high pressure vapor (state 1) enters the compressor 2 and is compressed to condenser pressure in the superheated state (state 2). Then, the flow is mixed with outlet flow of compressor 1 (state 3) in mixer and then the mixed flow enters the condenser (state 4), where the working fluid is cooled at condenser to the saturated liquid (state 5) by environment cold water stream circulation. The saturated liquid is divided into two streams. One stream flows to the first expansion valve (EV1) (state 8), and then is expanded to evaporator 1 pressure (state 9). This flow is then enters the evaporator 1 by producing specific amount of cooling capacity for freezing applications (-15 ). The saturated vapor (state 10) leaves the evaporator 1 and then enters the compressor 1 to be compressed to the superheated state (state 3), consuming specific amount of power for this purpose. Another part of the stream (state 6) enters the EV2, and

then is expanded to a two-phase flow at evaporator 2 pressure (state 7). This stream is then enters the evaporator 2 to produce specific amount of refrigeration capacity for airconditioning purposes (5 ). Then, the saturated vapor leaves the evaporator 2 (state 1) and enters the compressor 2 (state 1), completing the BDB-VCRC system operation. To enhance the performance of the proposed cycle based on thermodynamics and thermoeconomics viewpoints, ejector expanders are used in place of expansion valves. Doing this so, not only the refrigeration capacities (for both applications) are increased, but also the consumed powers by both compressors are decreased, resulting in performance enhancement of the basic system based on the first and second laws of thermodynamics [24, 25]. With this respect, schematic diagram of ejector expander DB-VCRC (EEDB-VCRC) system is shown in Fig. 2. As figure indicates, two ejectors and two separators are added to the basic system (Fig. 1(a)), where the expansion valves 1 and 2 are replaced by two-phase ejectors 1 and 2, respectively. In addition, since the outlet flows of the ejectors are two-phase flows, separator is employed at these streams. Doing this so, one part of the outlet liquid of condenser enters into the ejector 1 (state11) by experiencing a specific amount of pressure drops, and then draws the two-phase secondary flow into the ejector 1 (state 16). These two fluids are then mixed at mixing chamber by rising up its pressure into the mixing pressure. The mixed flow is then diffused into the state 12 through an isentropic process. The two-phase flow enters the liquid-vapor separator (separator 1) which separates two phases into the saturated vapor (state 13) and the saturated liquid (state 14). The saturated vapor enters the compressor 1, completing low-pressure loop operation, while the saturated liquid goes through the EV 1 by losing its pressure in an isenthalpic process (state 15). The outlet flow evaporates into the saturated vapor through the evaporator 1 by producing refrigeration for freezing applications, and then enters the ejector 1. Meanwhile, the rest of the condenser outlet liquid enters the ejector 2 (state6) by experiencing a specific amount of pressure drops, and then draws the

secondary flow (state 10) into the mixing chamber by rising up its pressure into the mixing pressure. Then, the mixed flow is diffused into a two-phase flow (state 7) through an isentropic process, and then enters the separator 2 in order to be separated into the saturated vapor (state 1) and saturated liquid (state 8). The saturated vapor enters the compressor 2, completing high-pressure loop thermodynamic operation, while the saturated liquid goes through the EV 2 by losing its pressure in an isenthalpic process (state 9). The outlet flow then evaporates into the saturated vapor through the evaporator 2 by producing refrigeration for air-conditioning applications, and then enters the ejector 2 (state 10), completing thermodynamic operation of the EEDB-VCRC system.

3. Thermodynamic and thermoeconomic analysis 3.1.Thermodynamic assumptions To model the proposed systems from thermodynamics viewpoint, following assumptions are made: 1. Systems are simulated under steady state condition. 2. The working fluid leaving the condenser, evaporators, and separators outlets is saturated. 3. The flow across the expansion valves is assumed isenthalpic. 4. The compressors operated with specific value of isentropic efficiency which is function of their corresponding compression ratio (CR)[43, 44]. 5. Water-glycol mixture with 30/70 percentage is used for freezing protection in evaporator 1. This percentage is believed to be applicable for temperature up to -16 6. The pressure drops in pipelines and the heat exchangers are neglected. 7. Kinetic energy at the inlet and outlet of all components is neglected.

[45].

8. The rate of chemical exergy is neglected through the simulation because of rare chemical reactions happening in organic materials and its negligible value compared with the physical exergy[46]. 9. All outer surface of the systems is at constant reference temperature, thus the rate of exergy loss can be neglected[46]. 3.2.Ejector mathematical modeling One dimensional constant-pressure mixing ejector model is used for mathematical modeling of ejector which is taken into account from our previous studies[25]. To simplify analysis of the ejector, some assumptions are taken into account as follows [25, 47, 48]: 

Flow inside the ejector is one dimensional.



Internal chamber of ejector is assumed adiabatic.



The motive and suction streams reach the same pressure at the inlet of the constant area mixing section of ejector and no mixing occurs before the mixing section.



Kinetic energy of primary and secondary flows at the inlet and outlet of ejector is neglected.



Effect of viscosity and mixing losses is considered in terms of nozzle, mixer, and diffuser isentropic efficiencies by 90%, 85%, and 85%, respectively.

In the nozzle, the primary flow velocity (

) can be neglected. In this case, the velocity of

outlet flow of nozzle can be expressed as:

where,

is the primary flow ideal enthalpy under isentropic expansion condition and

is the nozzle isentropic efficiency.

The mass entrainment ratio of the ejector is defined as the mass flow rate of the secondary flow (

) to the primary flow (

in which, both

and

):

are in kg/s.

Momentum conservative equation in the mixer can be expressed as:

Neglecting secondary flow velocity ( the velocity of ideal mixed flow (

) compared with the primary flow velocity ( ) can be calculated as:

The mixer isentropic efficiency then can be written as:

Thus, the real velocity of the mixed flow can be expressed as:

Energy conservative equation for the mixer can be applied as:

where, the mixed flow enthalpy can be calculated from the following relation:

),

In the mixing chamber, the kinetic energy of the mixed flow is converted into pressure energy. Neglecting velocity of the mixed flow at outlet of diffuser and employing diffuser isentropic efficiency, one can obtain real enthalpy of the mixed flow in terms of:

where, and

is the ideal enthalpy of the mixed flow under isentropic expansion conditions is the nozzle isentropic efficiency.

In accordance to the above mentioned equations, the ejector mass entrainment ratio can be expressed as:

This ratio is one of the most influential parameters in the modeling of ejector. The schematic of ejector and pressure losses along with velocity profile throughout the ejector is illustrated in Fig. 3. 3.3.Energy analysis From the first law of thermodynamics, once the mass and energy balance equations are applied to each component of system, all states thermodynamic properties can be specified thereafter. The general form of the steady state governing equations for mass and energy analysis of a cycle can be written as follows:

Some detail of the mass and energy balance equations of different components of the proposed systems are given in Appendix A. 3.4.Exergy analysis Entropy generation for a fixed control volume can be expressed by the following equation [46]:

where,

represents the heat transfer rate at the boundary location of the control volume and

is the instantaneous temperature. Exergy of a system is defined as the maximum theoretical useful work which can be obtained as the system interacts to equilibrium. Considering assumption number 8 in section 3.1, the overall exergy of the proposed system for different working fluids equals to the physical exergy rate [46]:

in which,

are specific enthalpy and entropy of the substance, respectively, while

are those parameters at reference state of known pressure and temperature of (

).

The general form of the exergy balance equation for any component of a system can be expressed as [46]:

where,

is the exergy destruction rate of kth component which can be defined by applying

the Gouy-Stodala theorem as follows [49]:

In exergy analysis, two useful concepts by the name of fuel and product can be introduced for each component. Exergy rate of product is defined as expected producible maximum theoretical work for a system, while exergy rate of fuel can be defined as the maximum required theoretical work for this production. Based on this definition, exergy balance equation can be also expressed as[46]:

in which,

and

the other hand,

are the rates of generated product and supplied fuel, respectively. On and

are the rates of exergy loss and exergy destruction, respectively.

Considering assumption number 9 into account, the Eq. (17) can be re-written as follows:

The exergy efficiency ( (

) is defined as the ratio of product exergy (

) to the fuel exergy

)[46, 49]:

Another important parameter in related to the system inefficiencies is the exergy destruction ratio, which is defined as the ratio of exergy destruction of element k ( exergy destruction of the system (

) to the overall

):

Some detail of the exergy balance equations of different components of the proposed systems are given in Appendix A. 3.5.Exergoeconomic analysis

Exergoeconomics (or thermoeconomics) is a branch of engineering which combines two concepts of exergy and economic to give more information for system designers which are not available through conventional economic evaluation [46]. In other word, exergoeconomic analysis is considered as exergy-aided cost minimization. In order to calculate the total cost per exergy unit of product of the proposed systems, economic analysis based on the obtained exergy parameters is conducted. With this respect, cost balance equations as well as the auxiliary equations for each component of the systems are specified. The cost balance equation states that the sum of cost rates of all exiting exergies is equal to the sum of cost rates of all entering exergies plus the cost rate associated with capital investment ( operating and maintenance (

) and

) [46]:

where,

here,

are the average costs per unit of exergy in

for inlet

flow, outlet flow, power and heat transfer of the kth component of a system, respectively. To calculate the cost of exergy destruction in each component, we have [46]:

where,

denotes the unit cost of product of the kth component of system which can be

expressed as:

In the same vein, the unit cost of supplied fuel of the kth component of system can be written as:

The total cost rate of the kth component is the sum of the capital investment ( operating and maintenance (

) and

) [46]:

The cost balance equation (Eq. (21)) can also be expressed in terms of the fuel and product cost rates as follows:

It is worthy to mention that the cost balances are generally written so that all terms are positive [46]. In order to convert the capital investment into the cost rate, the following equation is applied [46]:

where,

is the purchased equipment cost of the equipment ,

hours that the unit operates and is:

,

is the annual number of

is the maintenance factor and is:

[47, 50]. CRF is the capital recovery factor which is calculated in the following form:

where,

is the interest rate and it is equal to

cycles’ components and it is equal to

and [47, 50].

is the expected life of the proposed

For evaluation of the investment costs of equipment of the system, investment costs of each component are calculated. These components are: compressors, expansion valves, and heat exchangers. The investment cost of the ejectors and separators could be neglected, since the cost of this equipment is small compared to the other components. For the heat exchangers, following power-law relation is employed:

Considering the logarithmic mean temperature difference ( transfer coefficient (

) and the overall heat

), the heat exchanger area can be obtained from the heat transfer

equation as:

For the year 2000, the reference costs and the overall heat transfer coefficient for heat exchangers is listed in Table 1. With this respect,

in Eq. (30) is assumed to be

[47, 50]. The investment cost of a compressor can be expressed as follows:

Finally, for an expansion valve, the investment cost can be expressed in the form of:

where,

is the mass flow rate of the refrigerant passes from the expansion valve.

All the above calculated cost data at the reference year must be updated to the original year by the following relation:

The cost balance and auxiliary equations for each component of the proposed systems are given in Appendix B. 3.6.Performance criteria The coefficient of performance (COP) for the both proposed systems can be expressed as:

where,

is the consumed power of compressor.

The COP improvement ratio according to the base system can be calculated from the following equation:

where,

and

are the COP of the ejector expander and basic DB-VCRC systems,

respectively. The exergy efficiency of the BDB-VCRC and EEDB-VCRC systems can be expressed respectively as:

The exergy efficiency improvement ratio according to the base system can be calculated from:

The total sum unit cost of the product (SUCP) for the proposed BDB-VCRC and EEDBVCRC systems can be expressed respectively as:

where,

and

in Eq. (40) and

and

in Eq. (41) are the cost rate of cold exergy

released at the evaporators in the BDB-VCRC and EEDB-VCRC, respectively. In addition, in Eq. (40) and

in Eq. (41) refer to the fictitious cost rates associated with the

dissipative component (i.e., condenser) of the BDB-VCRC and EEDB-VCRC systems, respectively. The SUCP improvement ratio according to the base system can be calculated from:

4. Model validation An appropriate code is written in Engineering Equation Solver (EES) software to show the accuracy of the mathematical manipulation of the equations. A steady-state mathematical model based on the discussed relations is developed and the predicted results are validated using the available experimental and numerical data. Various most related benchmarks are selected and simulated under constant internal and external conditions. In the first benchmark, ERC is considered and simulated and the results are compared with the experimental ones, presented by Smierciew et al.[37]. In this study, pressure of motive vapor

and suction pressure are assumed 0.77 MPa and 0.2 MPa, respectively. Also, superheating of motive vapor and suction vapor are assumed 8 K and 6.5 K, respectively. In addition, saturation temperature of motive vapor and evaporation are set at 55

and 7 , respectively.

Under these conditions and using isobutane as working fluid, the results of this simulation are in good agreement with those of the Ref.[37] (Table 2). In the second problem, VCRC and EERC are considered and simulated under some conditions and results are compared with the experimental ones, presented by Sag et al. [24]. These conditions are as follows. The condenser and evaporator temperatures are set into 40 and 5 , respectively. R134a is used as working fluid in both VCRC and EERC systems. Also, the temperature and volumetric flow rates of the water flowing to the condenser and brine fluid flowing to the evaporator were kept constant. Moreover, the outlet flow of condenser and evaporator are assumed saturated. Under these conditions, the results are presented in Table 2, which also show a good agreement with this literature. In the third case study, the ejector (as a control volume) is considered and the results are compared with those of Huang et al.[51]. Table 3 indicates that the results of this simulation are in good agreement with those of these scholars, too. In this simulation, ejector mass entrainment ratio for various temperatures and pressures of the primary and secondary flows is calculated and compared with the 1D model and model presented by Huang et al.

5. Working fluid selection Refrigeration systems provide many benefits to industrialization world. However, these benefits bring many environmental consequences which are directly stemmed from working fluid selection. Because of many environmental concerns, some factors such as global warming potential (GWP), ozone depleting potential (ODP), and life-cycle climate performance (LCCP) have become important. Even though some class of working fluids has

favorable performance and/or environmental aspects, none provide a perfect solution. The main problems with natural working fluids include flammability, toxicity, high pressure, or in some cases a lower efficiency. A refrigerant must satisfy some basic requirements related to safety, environmental properties, chemical stability, thermodynamic properties, and so on. There are no setoff optimum characteristics, and hence a tradeoff must be considered. Hydrocarbons generally have good thermodynamic properties since they are constituents of natural gas and petroleum. Hydrocarbons with a wide range of boiling points have zero ODP, low GWP, and low toxicity. However, they are highly flammable that is their main impediment to their wider utilization. An earlier utilization of the chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) had resulted in phasing out these group working fluids utilization under Montreal Protocol due to their adverse environmental impacts related to ozone depletion. Properties of CFCs and HCFCs make them the main contributor to ozone depletion since they contain chlorine. They are relatively inexpensive chemicals and have significant atmospheric lifetimes[52]. A sustainable alternative for HCFs can be natural refrigerants such as R717 which are widely distributed in nature or synthetic refrigerants such as R600a and R290. In the amounts used in refrigeration, their greenhouse gas emissions have no or negligible impact on the climate. Due to this fact, R600a accounts for more than one-third of global production[52]. In this paper, four working fluids, namely, R717, R290, R600a, R134a are examined and suggested based on their thermophysical, safety, and environmental properties as well as energy and exergy efficiencies. Table 4 listed some useful thermophysical, safety, and environmental data for suggested working fluids. From thermodynamics, thermoeconomics,

and environment viewpoints, among all proposed working fluids, R717 is highly recommended due to its low value of GWP, high performance, and low value of SUCP.

6. Results and discussion In order to simulate the proposed novel refrigeration systems thermodynamically, some input thermodynamic data are required. Table 5 listed some required input data for simulation of the systems, where the comparison will be conducted to show the effect of ejector expander’s utilization in dual-loop bi-evaporator refrigeration systems under a constant condition. Thermodynamic properties and costs of the streams for the proposed BDB-VCRC and EEDB-VCRC systems using R717 are presented in Tables 6 and 7, respectively. These properties are: temperature, pressure, enthalpy, entropy, mass flow rate, total exergy rate, cost rate, and cost rate per unit of exergy. Table 8 presents the results of thermodynamic and thermoeconomic evaluations of the proposed refrigeration systems for different working fluids. As table indicates, using ejector expanders in place of expansion valves, the freezing and air-conditioning capacities are increased 10.09% and 1.93% for R717, 23.3% and 14.24% for R290, 32.68% and 1.39% for R600a, and 34.29% and 1.83% for R134a, respectively. Therefore, the cooling capacity (freezing capacity plus air-conditioning capacity) is improved by 4.41%, 17.07%, 10.85%, and 11.63% by the use of ejector expanders in place of expansion valves for R717, R290, R600a, and R134a, respectively. This augmentation is mainly contributed to the low-pressure loop of the proposed dual-loop bi-evaporator refrigeration systems. In addition, the consumed power by compressors is also decreased by 32.98%, 20.95%, 18.88%, and 11.74% for R717, R290, R600a, and R134a, respectively, as expansion valves are replaced by ejector expanders. As a result of these variations, the COP and exergy efficiency of the BDB-VCRC system are improved by 22.35% and 57.97% for R717, 48.07%

and 50.9% for R290, 36.69% and 48.14% for R600a, and 26.46% and 33.3% for R134a, respectively. In comparison with the single-loop VCRC system, performance enhancement of the dual-loop VCRC by using ejector expander is considerably higher based on the first and second laws of thermodynamics. This can be mainly attributed to the dominant existence of throttling loss in each loop of system [24, 30, 31]. Therefore, it is highly recommended to use EEDB-VCRC system instead of BDB-VCRC system for producing cooling capacity at two different temperature levels. Another significant indication of Table 8 is that the cost of system associated with the cooling production is also reduced as ejector expanders are used in place of expansion valves in the BDB-VCRC system. With this regard, the SUCP improvement ratio is calculated 11.03%, 26.51%, 36.8%, and 23.16% for R717, R290, R600a, and R134a, respectively. Table 9 listed some component cost rates and exergoeconomic factors for the proposed BDBVCRC and EEDB-VCRC systems under the considered constrained input parameters for different working fluids. These parameters are exergy destruction ratio ( destruction rate (

), cost of exergy

), and investment cost ( ). The cost of exergy destruction for the ith

component of the cycle can be calculated from Eq. (23). As table indicates, among all components, compressor 1 accounts for the largest exergy destruction rate in the BDB-VCRC system, while evaporator 1 accounts for the largest exergy destruction rate in the EEDBVCRC system. In addition, it is found that evaporator 2 had the highest investment cost when R717 and R290 are selected. However, when R290 and R134a are used, compressor 2 had the highest investment cost. Even though employing some extra components in the case of using ejector expanders in place of expansion valves increases the investment cost rate of the overall system for some working fluids, however, this investment cost augmentation can be considered negligible for such high enhancement in the overall performance of system based on the thermodynamics viewpoint.

Another significant indication of Table 9 is that the highest cost of exergy destruction corresponds to the evaporators. This is due to the fact that evaporators have relatively high exergy destruction and cost of the fuel. In addition, the total cost of exergy destruction is decreased considerably from 3720 $/yr to 1062 $/yr (71.45%), 5639 $/yr to 2462 $/yr (56.33%), 6418 $/yr to 2509 $/yr (60.9%), and 8615 $/yr to 5211 $/yr (39.51%) for R717, R290, R600a, and R134a, respectively, when ejector expanders are used in place of expansion valves in the proposed BDB-VCRC system. Thus, using ejector as an expansion device in dual loop bi-evaporator refrigeration system will result in more enhancements due to the dominant effect of throttling loss during expansion process, where the amount of enhancement highly depends on the working fluids, too. Fig. 4 illustrates and compares the exergy destruction rate of each component of system and overall system for BDB-VCRC and EEDB-VCRC systems, using R717 as working fluid. As figure indicates, the total exergy destruction rate of BDB-VCRC system can be decreased by 58.53% as ejector expanders are employed in place of expansion valves. Nearly all components’ exergy destruction rate is decreased by the use of ejector expansion device, while it is more highlighted in the expansion valves. As shown, the exergy destruction rates of expansion valves 1 and 2 are decreased by 91.66% and 76.24%, respectively. Therefore, use of ejectors as expansion device in place of conventional expansion valves can decrease the irreversibility of dual-loop refrigeration systems more considerably.

7. Parametric study In the real operation of refrigeration cycles, the performance of the system can be affected by any disturbances caused by external forces which may act on the system whether directly or indirectly. These disturbances may result in significant deviation in the main performance parameters of refrigeration systems. Therefore, obtaining a comprehensive knowledge from

effect of different key parameters on the main overall performance criteria may give a wide viewpoint for designers. Therefore, in this section, the effect of some key thermodynamic parameters including evaporators temperature and condenser temperature on the key thermodynamic performance criteria, including cooling capacity, COP, exergy efficiency and total SUCP of system are investigated, using R134a as working fluid. 7.1.The effect of condenser temperature on the systems Fig. 5 has been plotted to show the effect of condenser temperature on the main performance parameters, namely cooling capacity, COP, exergy efficiency and SUCP. As figure indicates, the performance of system is improved in all condenser temperature ranges by the use of ejector as expansion device in place of expansion valve based on the energy, exergy and exergoeconomic concepts viewpoints (as discussed in section 6). However, the main implication of Fig. 5(a) is that, an increase in the condenser temperature decreases the cooling capacity of both systems. This can be justified by the fact that an increase in the condenser temperature decreases the enthalpy difference through both evaporators, while affects the mass flow rates through the evaporators so slightly. As a result, both freezing and airconditioning capacities are decreased with the condenser temperature augmentation, and hence the cooling capacity is decreased thereafter. On the other hand, the consumed power by compressors is increased with condenser temperature augmentation. As a result of these two factors (decreasing of cooling capacity and increasing of compressor power), the COP is decreased for both proposed systems as condenser temperature increases. Meanwhile, the variation of exergy efficiency and SUCP of system with condenser temperature is illustrated in Fig. 5(b). As explained above, since the cooling capacity is decreased with condenser temperature augmentation, thus the cooling exergy is decreased throughout this variation, too. In the same vein, an augmentation in the compressor power

with an increase in the condenser temperature will result in more supplied exergy of the overall system, and hence the supplied exergy of the overall systems are increased. Due to these two factors (reduction in cooling exergy and augmentation of supplied exergy of the overall system), the exergy efficiency of both systems are decreased as condenser temperature increases. Moreover, the results of cost analysis indicated that the sum unit cost product of system due to the cooling production is increased as condenser temperature increases. However, the augmentation rate for the ejector expander dual-loop bi-evaporator vapor compression refrigeration system is considerably lower than that of the basic system. An increase in the condenser temperature decreases the freezing and air-conditioning exergies along with their cost rates, simultaneously. However, the fictitious cost rate associated to the condenser is increased considerably as condenser temperature increases which is dominant over all above mentioned variations. As a result, the SUCP of both systems associated with cooling production is increased with an increase in the condenser temperature. 7.2.The effect of evaporator 1 temperature on the systems The effect of evaporator 1 temperature on the cooling capacity, COP, exergy efficiency and SUCP of both BDB-VCRC and EEDB-VCRC systems is plotted in Figs. 6. As this figure indicates, performance of the BDB-VCRC system is improved in all evaporator 1 temperature ranges by the use of ejector as expansion device in place of expansion valve based on the energy, exergy and exergoeconomic concepts viewpoints. According to Fig. 6(a), an increase in the evaporator 1 temperature increases the cooling capacity of both BDBVCRC and EEDB-VCRC systems. This is mainly due to the fact that an increase in the evaporator 1 temperature increases the enthalpy difference through the first evaporator, while the enthalpy difference through the second evaporator is remained constant throughout this

variation. In addition, the mass flow rate through evaporators 1 and 2 is increased and decreased with evaporator 1 temperature augmentation, respectively. As a result, the freezing capacity is increased, while air-conditioning capacity is decreased with an increase in the evaporator 1 temperature. Since the air-conditioning capacity reduction rate is dominated by the augmentation rate of freezing capacity, hence the cooling capacity is increased with an increase in the evaporator 1 temperature. On the other hand, the consumed power by compressors is decreased with evaporator 1 temperature augmentation. As a result of these two factors (increasing of cooling capacity and decreasing of compressor power), the COP will be increased for both proposed systems as evaporator 1 temperature increases. Meanwhile, the variation of exergy efficiency and SUCP of system with evaporator 1 temperature is illustrated in Fig. 6(b). As explained above, since the cooling capacity is increased with evaporator 1 temperature augmentation, thus the cooling exergy is increased throughout this variation, too. In the same vein, a reduction in the compressor power with an increase in the evaporator 1 temperature will result in less supplied exergy to the overall system, and hence the supplied exergy of the overall systems will be decreased. Due to these two factors (augmentation of cooling exergy and reduction in supplied exergy of the overall system), the exergy efficiency of both systems will be increased as evaporator 1 temperature increases. Moreover, the results of exergoeconomic shows that the SUCP of both proposed refrigeration systems is decreased as evaporator 1 temperature increases, however, the augmentation rate for the EEDB-VCRC system is considerably higher than that of the BDB-VCRC system. An increase in the evaporator 1 temperature decreases the air-conditioning exergy and its corresponding cost rate, while increases the freezing exergy and its cost rate. In addition, the fictitious cost rate associated with the condenser is increased considerably as evaporator 1 temperature increases. Interesting enough, the augmentation rate of the cost rates associated

with cooling production and fictitious part of system is dominated by the augmentation rate of the cooling exergy of systems. As a result, the SUCP of both systems will be decreased with an increase in the evaporator 1 temperature. 7.3.The effect of evaporator 2 temperature on the systems The effect of evaporator 2 temperature on the cooling capacity, COP, exergy efficiency and SUCP of both BDB-VCRC and EEDB-VCRC systems is plotted in Figs. 7. As figure indicates, performance of the BDB-VCRC system is improved in all evaporator 2 temperature ranges by the use of ejector as expansion device in place of expansion valve based on the energy, exergy and exergoeconomic concepts viewpoints. According to Fig. 7(a), an increase in the evaporator 2 temperature increases the cooling capacity of both BDBVCRC and EEDB-VCRC systems. This is mainly due to the fact that an increase in the evaporator 2 temperature increases the enthalpy difference through the second evaporator, while no change of enthalpy difference through the first evaporator is experienced throughout this variation. In addition, the mass flow rate through the evaporators 1 and 2 is decreased and increased with evaporator 2 temperature augmentation, respectively. As a result, the freezing capacity is decreased, while air-conditioning capacity is increased with an increase in the evaporator 2 temperature. Since the freezing capacity reduction rate is dominated by the augmentation rate of air-conditioning capacity, hence the cooling capacity will be increased with an increase in the evaporator 2 temperature. On the other hand, the consumed power by compressors is decreased with augmentation of the evaporator 2 temperature. As a result of these two factors (increasing of cooling capacity and decreasing of compressor power), the COP will be increased for both proposed systems as evaporator 2 temperature increases.

Meanwhile, the variation of exergy efficiency and SUCP of system with evaporator 2 temperature is illustrated in Fig. 7(b). As explained above, since the cooling capacity is increased with augmentation of the evaporator 2 temperature, thus the cooling exergy will be increased throughout this variation, too. In the same vein, a reduction in the compressor power with an increase in the evaporator 2 temperature will result in less supplied exergy of the overall systems, and hence the supplied exergy of the overall systems will be decreased. Due to these two factors (augmentation of cooling exergy and reduction in supplied exergy of the overall systems), the exergy efficiency of both systems will be increased as evaporator 2 temperature increases. Moreover, the results of exergoeconomic shows that the SUCP of both proposed refrigeration systems is increased as evaporator 2 temperature increases. This is mainly because, an increase in the evaporator 2 temperature increases the air-conditioning exergy and its corresponding cost rate while decreases the freezing exergy along with its cost rate. In addition, the fictitious cost rate associated with the condenser is increased as evaporator 2 temperature increases. Due to reduction of the cooling exergy along with augmentation of cost rate associated with the cooling production and fictitious part of system, the SUCP of both systems will be increased with an increase in the evaporator 2 temperature.

8. Conclusions In this paper, two new basic and ejector expander dual-loop bi-evaporator vapor compression refrigeration cycles are proposed to produce cooling capacity at two different temperature levels for freezing and air-conditioning applications. The proposed systems consist of a high pressure and a low pressure loops each of which consumes equal portion of power. Four working fluids of R717, R290, R600a, and R134a are examined, where R717 is recommended as a good candidate from thermodynamics, thermoeconomics, and

environment viewpoints. The results indicated that, using ejector expanders in place of expansion valves, the freezing capacity, air-conditioning capacity, COP, exergy efficiency, and sum unit cost of cooling production of the basic proposed refrigeration system can be improved. In addition, a comprehensive parametric study is conducted leading to determine the main performance characteristics behavior of the proposed systems due to any unwanted disturbances. Some remarkable findings are summarized as below: 

Using R717 as working fluid and ejector expander in place of expansion valve, the freezing capacity, air-conditioning capacity, COP, exergy efficiency, and cost of cooling are enhanced 10.09%, 1.93%, 22.35%, 57.97%, and 11.03%, respectively.



Using R290 as working fluid and ejector expander in place of expansion valve, the freezing capacity, air-conditioning capacity, COP, exergy efficiency, and cost of cooling are enhanced 23.3%, 14.24%, 48.07%, 50.9%, and 26.51%, respectively.



Using R600a as working fluid and ejector expander in place of expansion valve, the freezing capacity, air-conditioning capacity, COP, exergy efficiency, and cost of cooling are enhanced 32.68%, 1.39%, 36.69%, 48.14%, and 36.8%, respectively.



Using R134a as working fluid and ejector expander in place of expansion valve, the freezing capacity, air-conditioning capacity, COP, exergy efficiency, and cost of cooling are enhanced 34.29%, 1.83%, 26.46%, 33.3%, and 23.16%, respectively.



For all working fluids it is observed that compressor 1 accounts for the largest exergy destruction rate in the BDB-VCRC system, whereas evaporator 1 accounts for the largest exergy destruction rate in the EEDB-VCRC system.



Using R717 and R290 in both systems, evaporator 2 had the highest investment cost, whereas, compressor 2 had the highest investment cost when R290 and R134a are used.



A higher COP and exergy efficiency can be obtained at lower condenser temperatures or higher evaporators temperatures, while a lower cost of product is attainable at lower condenser and evaporator 2 temperatures or at higher evaporator 1 temperatures.



The total cost of exergy destruction is decreased considerably from 3720 $/yr to 1062 $/yr (71.45%), 5639 $/yr to 2462 $/yr (56.33%), 6418 $/yr to 2509 $/yr (60.9%), and 8615 $/yr to 5211 $/yr (39.51%) for R717, R290, R600a, and R134a, respectively, when ejector expanders are used in place of expansion valves in the proposed BDB-VCRC system.



Using R717, the exergy destruction rate of expansion valves 1 and 2 are decreased by 91.66% and 76.24%, respectively. Therefore, use of ejector as expansion device in place of conventional expansion valves can decrease the irreversibility of dual-loop refrigeration systems more considerably.

Appendix A: Applying Eqs. (1-20) to each component of the BDB-VCRC and EEDB-VCRC systems, the mass, energy, and exergy balance equations for each component of the proposed systems can be obtained. Tables A.1 and A.2 listed some required mass, energy, and exergy balance equations for the BDB-VCRC and EEDB-VCRC systems.

Appendix B: To investigate the proposed systems from economics viewpoint, the cost balance equations along with auxiliary equations of each component of the systems must be obtained. Using Eqs. (21-34), cost balance and auxiliary equations are calculated and listed in Tables B.1 and B.2, respectively.

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Figure 1 Schematic diagram of: (a) the BDB-VCRC system and (b) its corresponding T-s diagram. Figure 2 Schematic diagram of: (a) the EEDB-VCRC system and (b) its corresponding T-s diagram. Figure 3 schematic diagrams of the ejector and pressure and velocity losses through it. Figure 4 Comparison of the overall exergy destruction rate in different components of BDBVCRC and EEDB-VCRC systems, using R717. Figure 5 The effect of condenser temperature on the: (a) cooling capacity and COP and (b) exergy efficiency and total SUCP for the BDB-VCRC and EEDB-VCRC systems, using R134a. Figure 6 The effect of evaporator 1 temperature on the: (a) cooling capacity and COP and (b) exergy efficiency and total SUCP for the BDB-VCRC and EEDB-VCRC systems, using R134a. Figure 7 The effect of evaporator 2 temperature on the: (a) cooling capacity and COP and (b) exergy efficiency and total SUCP for the BDB-VCRC and EEDB-VCRC systems, using R134a.

(a)

3 4

T [K]

2 5,6,8

1

7

10

9 0.2

0.4

0.6

s [kJ/kg-K] (b) Figure 1

0.8

(a)

3 4

T [K]

2 5,6,11

8

7

9

14

1 10

12

13 16

15 0.2

0.4

0.6

s [kJ/kg-K] (b) Figure 2

0.8

Figure 3

Exergy destruction (kW) 2.6835

TOTAL

4.2544 0.05996 0.2524 0.02453 0.2943 0.3916 0.6861 0.5632

E.V 2/E.V 2+Ejector 2 E.V 1/E.V 1+Ejector 1 Compressor 2 Compressor 1

1.047 0.4122 0.4044

Evaporator 2

0.7957 0.7223

Evaporator 1

0.4152

Condenser 0

0.5

0.8485 1

1.5

2

EEDB-VCRC

2.5

3

3.5

4

4.5

BDB-VCRC

Figure 4

Cooling capacity, BDB-VCRC

Cooling capacity, EEDB-VCRC

COP, BDB-VCRC

COP,EEDB-VCRC

45

7

6 40

35

4

COP

Cooling capacity (kW)

5

3

30

2 25 1

20

0 300

305

310

315

320

325

330

Condenser temperature (K)

335

340

345

350

(a)

Exergy efficiency, BDB-VCRC

Exergy efficiency, EEDB-VCRC

SUCP, BDB-VCRC

SUCP,EEDB-VCRC

30

650 600

25

20

500 450

15 400 10

350 300

5 250 0

200 300

305

310

315

320

325

330

Condenser temperature (K)

(b) Figure 5

335

340

345

350

SUCP ($/GJ)

Exergy efficiency (%)

550

Cooling capacity, BDB-VCRC

Cooling capacity, EEDB-VCRC

COP, BDB-VCRC

COP,EEDB-VCRC

45

5.5

44 43

5

41

4.5

COP

Cooling capacity (kW)

42

40 39

4

38 37

3.5

36

35

3 235

240

245

250

255

Evaporator 1 temperature (K)

(a)

260

265

270

Exergy efficiency, EEDB-VCRC

SUCP, BDB-VCRC

SUCP,EEDB-VCRC

24

550

22

500

20

450

18

400

16

350

14

300

12

250

10

200 235

240

245

250

255

Evaporator 1 temperature (K)

(b) Figure 6

260

265

270

SUCP ($/GJ)

Exergy efficiency (%)

Exergy efficiency, BDB-VCRC

Cooling capacity, EEDB-VCRC

COP, BDB-VCRC

COP,EEDB-VCRC

45

7.5

44

7

43

6.5

42

6

41

5.5

40

5

39

4.5

38

4

37

3.5

36

3

35

2.5 255

260

265

270

275

Evaporator 2 temperature (K)

(a)

280

285

290

COP

Cooling capacity (kW)

Cooling capacity, BDB-VCRC

Exergy efficiency, BDB-VCRC

Exergy efficiency, EEDB-VCRC

SUCP, BDB-VCRC

SUCP,EEDB-VCRC 550

24 500 22 450

400 18 350

16

300

14

250

12

200

10

150 255

260

265

270

275

Evaporator 2 temperature (K)

(b) Figure 7

280

285

290

SUCP ($/GJ)

Exergy efficiency (%)

20

Tables:

Table 1 The overall heat transfer coefficient and reference cost for heat exchangers. Component Reference cost ($) Condenser 8000 1.1 Evaporator 16000 0.9

Benchmark (a)

ERC

(b) VCRC

EERC

Table 2 Model validation between present work and experiments. Parameter Present work Literature Relative error (%) Ref. [37] Vapor generator duty 8.713 9 3.18 1.706 1.75 2.51 Cooling capacity 10.826 11.28 4.02 Condenser load Pump power 0.01901 0.02 4.95 0.2422 0.24 0.91 Mass entrainment ratio 0.1954 0.19 2.84 Coefficient of performance Ref.[24] 4.13 4.3 3.9 Cooling capacity 1.409 1.52 7.3 Compressor power Coefficient of performance ( ) 2.805 2.82 0.53 4.551 4.3 5.8 Cooling capacity 1.402 1.35 3.8 Compressor power 3.188 3.183 0.15 Coefficient of performance ( )

Table 3 Ejector modeling validation between present work and Huang et al. [51]. 1-D model

Huang et al.

Present work

ARD1 * ARD2 ** (%) (%)

0.604;95

0.04;8

42.1

0.1554 0.1859

0.1621

4.31

12.8

0.538;90

0.04;8

38.9

0.2156 0.2246

0.2201

2.08

2

0.465;84

0.04;8

35.5

0.2880 0.2880

0.2804

2.63

2.63

0.4;78

0.04;8

32.5

0.3525 0.3257

0.3334

5.41

2.36

0.604;95

0.0473;12

42.5

0.2573 0.2350

0.2402

6.64

2.21

0.538;90

0.0473;12

39.5

0.3257 0.2946

0.3023

7.18

2.91

0.465;84

0.0473;12

36

0.4147 0.3398

0.3854

7.04

13.41

*Absolute relative difference between present work and 1-D model.

**Absolute relative difference between present work and Huang et al.

Table 4 Thermophysical, safety, and enviromental data of the applied working fluids. Normal Critical Critical Selected Chemical boiling GWP ASHARAE temperature pressure Working point formula (100yr) Safety code fluids ( ) ( ) ( ) R717 NH3 405.4 113.3 239.8 <1 B2 R290 C3H8 369.8 42.47 231.1 3.3 A3 R600a C4H10 408.1 36.47 261.3 3 A3 R134a C2H2F4 374.2 40.59 247.1 1430 A1

Table 5 Some required input parameters for simulation. Parameter Reference temperature, Reference pressure, Mass flow rate of condenser inlet water, Condenser temperature, (K)

value 290 0.101 0.5 310 258 278 298 273 283 5 3

Evaporator 1 temperature, Evaporator 2 temperature, Condenser inlet water temperature, Evaporator 1 inlet water temperature, Evaporator 2 inlet water temperature, Pinch point temperature difference of evaporator 1, Pinch point temperature difference of evaporator 2, Nozzle efficiency of ejector,

85

Mixer efficiency of ejector,

90

Diffuser efficiency of ejector,

85

Table 6 Thermodynamic properties and costs of the streams for the proposed BDB-VCRC system, using R717. Strea m 1

Workin g fluid R717

2

R717

3

R717

4

R717

5

R717

278 363. 5 443. 5 387. 4 310

0.5132

1467

5.558

0.02511

5.62

601.2

107

1.424

1644

5.653

0.02511

9.382

1012

107.9

1.424

1848

6.158

0.01102

4.743

431.6

90.99

1.424

1706

5.818

0.03613

14.01

1444

103.1

1.424

375.1

1.596

0.03613

10.15

1046

103.1

6 7 8 9 10

R717 R717 R717 R717 R717

310 278 310 258 258

1.424 0.5132 1.424 0.2347 0.2347

375.1 375.1 375.1 375.1 1444

1.596 1.63 1.596 1.688 5.831

0.02511 0.02511 0.01102 0.01102 0.01102

11

Water

298

0.101

104.2

0.3648

0.5

12 13 14

Water Water Water Waterglycol Waterglycol

321 283 281

0.101 0.101 0.101

200.4 41.46 33.08

0.6758 0.1487 0.119

273

0.101

-333.1

263

0.101

-354.1

15 16

727.1 727.7 319.3 319.6 153

103.1 107 103.1 114 114

0

0

0.5 3.272 3.272

7.055 6.802 3.098 2.804 1.342 0.226 6 3.236 1.176 1.954

527.1 0 859.2

162.9 0 439.7

-1.222

0.5597

12.98

0

0

-1.299

0.5597

13.72

432.7

31.53

Table 7 Thermodynamic properties and costs of the streams for the proposed EEDB-VCRC system, using R717. Stream 1 2 3 4 5 6 6a 7 7a 8 9 10 10a 11 11a 12 12a 13 14 15 16 16a 17 18 19 20 21 22

Working fluid R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 R717 Water Water Water Water Waterglycol Waterglycol

288.1 341.5 395.6 356.4 310 310 272.8 288.2 275.2 288.2 278 278 272.8 310 254.7 267.8 258.9 267.6 0.001548 0.01874 0.5117 254.7 298 321 283 281

0.728 1.424 1.424 1.424 1.424 1.424 0.423 0.73 0.464 0.729 0.5132 0.5132 0.424 1.424 0.204 0.35 0.244 0.3479 0.3487 0.2347 0.2347 0.204 0.101 0.101 0.101 0.101

1476 1585 1727 1626 375.1 375.1 362.5 888.8 859.2 270.1 270.1 1467 1444 375.1 348.5 893.1 868.4 1456 174.9 174.9 1444 1427 104.2 200.4 41.46 33.08

5.435 5.484 5.871 5.6 1.596 1.596 1.596 3.395 3.395 1.248 1.252 5.558 5.558 1.596 1.596 3.589 3.589 5.694 0.9075 0.9114 5.831 5.831 0.3648 0.6758 0.1487 0.119

0.02747 0.02747 0.011 0.03847 0.03847 0.02747 0.02747 0.05081 0.05081 0.02335 0.02335 0.02335 0.02335 0.011 0.011 0.02123 0.02123 0.011 0.01023 0.01023 0.01023 0.01023 0.5 0.5 3.335 3.335

7.385 9.975 4.324 14.23 10.81 7.718 7.37 13.87 12.36 6.46 6.432 5.226 4.674 3.09 2.797 4.685 4.162 1.906 2.866 2.855 1.245 1.074 0.2266 3.236 1.199 1.992

647.9 1000 390 1390 1055 753.6 1215 566.8 567.3 461 301.8 409 163.3 245.7 245.9 107.2 0 497.6 0 847.5

87.73 100.2 90.2 97.64 97.64 97.64 87.6 87.73 88.21 88.21 97.64 87.3 85.71 85.71 86.14 86.14 0 153.8 0 425.5

273

0.101

-333.1

-1.222

0.6165

14.3

0

0

263

0.101

-354.1

-1.299

0.6165

15.12

420.7

27.83

Table 8 Thermodynamic and thermoeconomic evaluation results for BDB-VCRC and EEDB-VCRC systems. R290

R717 Performance parameters Compressor 1 work, (kW) Compressor 2 work, (kW) Freezing capacity, (kW) Air-conditioning capacity, (kW) Cooling capacity, (kW) Condenser duty, (kW) Coefficient of performance, Exergy efficiency, (%) Sum unit cost of product of system, SUCP ($/GJ) Cooling improvement ratio, (%) COP improvement ratio, (%) Exergy efficiency improvement ratio, (%) SUCP improvement ratio, (%)

BDB-VCRC system

EEDB-VCRC system

4.448

2.982

4.448

2.982

11.79

12.98

27.42

27.95

39.2

40.93

48.1

48.1

4.407

5.392

17.06

26.95

116

R600a

BDB-VCRC system 4.49

EEDB-VCRC system 3.549

BDB-VCRC system 4.521

EEDB-VCRC system 3.667

4.49

3.549

4.521

3.667

12.36

15.24

11.81

15.67

26.75

30.56

27.25

27.63

39.12

45.8

39.06

43.3

48.1

48.1

48.1

48.1

4.356

6.45

4.319

5.9

17.02

25.69

16.74

24.8

212.3

156

209.5

132.4

103.2 17.07

EEDB-VCRC system

4.573

4.036

4.573

4.036

11.75

15.78

27.2

27.7

38.95

43.48

48.1

48.1

4.259

5.386

16.5

22

322

247.4

11.63 48.07

36.69

50.9

48.14

57.97 11.03

BDB-VCRC system

10.85

4.41 22.35

R134a

26.46 33.3

26.51

36.8

23.16

Table 9 Component cost rates and exergoeconomic factors for the proposed BDB-VCRC and EEDB-VCRC systems. R290

R717 Compone nt Condense r Evaporato r1 Evaporato r2 Compress or 1 Compress or 2

BDB-VCRC system

EEDB-VCRC system

19.42

148.6

129.5

15.47

68.66

163. 2

16.53

422.8

266.1

29.65

411

282

9.22

446.6

732.7

15.36

440.5

23.95

85.73

167.4

20.98

52.8

15.7

75.01

300

14.59

53.2

EV 1

6.73

33.54

0.267

0.42

0.97

EV 2

5.77

27.01

0.609

1.07

2.55

Ejector 1 Ejector 2 Separator 1 Separator 2

-

-

-

0.49 1.15

30.53 80.71

741. 2 152. 2 277. 4 0.24 8 0.56 6 0 0

-

-

-

0.37

0.177

0

-

-

-

0.75

0.743

0

Total

-

3720

1596. 5

-

1062

161 7

BDB-VCRC system

3.29

73.37

17.09

822.7

8.93

578.7

23.86

242.7

15.79

214.2

17.16

281.9

13.61

202.3

-

516. 5 273. 9 722

R600a

EEDB-VCRC system

4.2

45.69

32.23

818.1

15.6

597.1

26.51

184.2

16.95

178.1

0.2

1.64

1.58

12.63

-

674. 8 104 7 1.15 9 2.30 8 -

0.28 2.14 0.05

-

-

-

-

5639

323 8

239. 1 310. 5 782

BDB-VCRC system

2.25

38.56

16.02

961.3

8.91

607.7

28.71

342.7

17.08

269.4

15.19

336.1

11.59

194.3

76.58 128.8 0.69

577. 5 101 9 0.95 8 2.12 8 0 0 0

-

0.08

0.99

0

-

2462

293 1

128. 4 266. 5 729. 9 738. 5 119 6 1.2

R134a

EEDB-VCRC system

2.93

34.42

35.94

945.4

12.48

585.3

23.88

235.5

18.07

217.1

1.26

10.68

0.23

2.518

-

2.49 5 -

2.2 0.40 0.06

-

-

-

-

6418

306 3

BDB-VCRC system

3.56

121.8

354

15.55

1307

8.65

762.7

28.39

563.1

16.88

464.3

14.63

498.9

11.88

347.6

4.41

25.4 129.3 0.633

731. 4 790. 1 105 2 1.34 8 1.96 4 0 0 0

376. 6 265. 6 729. 3 128 3 214 1 2.06

-

-

-

2.5

0.268

0

-

-

-

-

2509

299 9

-

8615

480 1

-

EEDB-VCRC system

4.37

105.9

453. 4

31.92

1363

317

12.4

735.9

29.39

475.4

19.53

409.8

0.13

2.49

1.86

0.30

5.65

3.53

8.67 1.9

170.8 35.4

0 0

0

188

0

1.3

24.98

0

-

5211

483 1

737. 3 125 3 206 5

Table A.1: Mass and energy balance equations employed for energy analysis of the BDBVCRC and EEDB-VCRC systems. Energy balance equations Component BDB-VCRC system EEDB-VCRC system = , = , Condenser = = = , = , Evaporator 1 = = = , = , Evaporator 2 = = = , = , , , Compressor 1 , , =

,

=

,

,

Compressor 2

, ,

EV 1 EV 2 Ejector 1 Ejector 2

-

Separator 1

-

Separator 2

-

,

See ejector modeling sub-section See ejector modeling sub-section = , = = , =

Table A.2: Exergy balance equations employed for exergy analysis of the BDB-VCRC and EEDB-VCRC systems. Exergy balance equations Component

Condenser Evaporator 1 Evaporator 2

BDB-VCRC system

EEDB-VCRC system

= = =

= = =

Compressor 1

=

=

Compressor 2

=

=

EV 1 EV 2 Ejector 1 Ejector 2 Separator 1

= =

= = = = =

-

57

Separator 2 Total system

=

= =

58

Table B.1: Cost balance equations employed for each component of the BDB-VCRC and EEDB-VCRC systems. Cost balance equation Component

BDB-VCRC system

Condenser Evaporator 1 Evaporator 2 Compressor 1 Compressor 2 EV 1 EV 2 Ejector 1 Ejector 2 Separator 1 Separator 2 Division point Mixing point

EEDB-VCRC system

= = =

= = =

= =

= = = =

= = -

= = = =

= =

= =

Table B.2: Required auxiliary equations for each component of the BDB-VCRC and EEDB-VCRC systems. Auxiliary equation Component

BDB-VCRC

Condenser Evaporator 1 Evaporator 2 Compressor 1 Compressor 2 Division point Separator 1 Separator 2

-

59

EEDB-VCRC