Comparative investigation and multi objective design

Heat and Mass Transfer https://doi.org/10.1007/s00231-018-2430-3

ORIGINAL

Comparative investigation and multi objective design optimization of a cascaded vapor compression absorption refrigeration system operating with different refrigerants in the vapor compression cycle Mert Sinan Turgut 1

&

Oguz Emrah Turgut 1

Received: 8 October 2017 / Accepted: 17 July 2018 # Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract This study aims to comparatively investigate the performance of a cascaded vapor compression absorption refrigeration system (CVCARS) operated with different refrigerants such as R1234yf, R134a, R717 and R290 in vapor compression cycle. Two design objectives are considered for performance evaluations. Total annual cost is the first design objective which includes investment and operational cost along with the social cost associated with carbon emissions. Exergy efficiency is the second considered objective which is related to thermodynamic issues. These problem objectives are individually and concurrently optimized by means of Artifical Cooperative Search metaheuristic algorithm and best results are compared for each cycle configuration. Single objective optimization results reveal that CVCARS working with R717 in vapor compression cycle has the lowest total annual cost whereas the maximum second law efficiency is obtained by the refrigeration system operated with R290 in vapor compression cycle. Following that, multi objective optimization is applied to acquire the Pareto optimal solutions which are nondominated to each other and no solution between them prevails over the other. Reputed decision making method TOPSIS is applied to choose the final best answer among the Pareto curve. It is seen that solution found by TOPSIS is skewed towards the minimum total annual cost and second law efficiency for each cycle configuration. Sensitivity analysis is then put into practice to observe the influences of variations of decision variables on design objectives as well as performance coefficients of the different cycles in the refrigeration system. List of symbols A Heat exchanger surface area (m2) ACS Artificial Cooperative Search Celec Electricity cost ($/kWh) Environmental cost ($/year) Cenv Cfuel Fuel cost ($/kWh) Investment cost ($) Cinv Operational cost ($) Coper Cp Specific heat at constant pressure (kJ/kg.K) Total annual cost ($/year) CT COP Coefficient of performance CRF Capital recovery factor CVCARS Cascaded vapor compression absroption refrigeration system d Tube diameter (m)

* Mert Sinan Turgut [email protected] 1

Mechanical Engineering Department, Ege University, 35040 Bornova/Izmir, Turkey

dH f g H h hfg i k m˙ m˙ CO2 N Ntube Npass P Pr Q˙ ; q R Re s T Tsat

Hyrdaulic diameter of annulus (m) Friction factor Gravitational acceleration (m/s2) Total annual operation hours Entalphy (kj/kg), Convective heat transfer coefficient (W/m2K) Latent heat of vaporization (kj/kg) Interest rate Thermal conductivity (W/m.K) Mass flow rate (kg/s) Amount of carbon dioxide emission (ton/year) Life time of the refrigeration system (N) Number of tube in heat exchanger Number of shell pass in heat exchanger Pressure (Pa) Prandtl number Heat transfer amount (kW) Fouling resistance (m2K/W) Reynolds number Entropy (kJ/kg.K) Temperature (°C - K) Saturation temperature (°C - K)

Heat Mass Transfer

Twall Wall temperature (°C - K) ΔTLMTD Logarithmic mean temperature difference U Overall heat transfer coefficient (W/m2K) v Working fluid velocity (m/s) VARS Vapor Absorption Refrigeration System VCRS Vapor Compression Refrigeration System W˙ Compressor or pump work (kW) x Mass concentration of absorbent in the solution Z Capital cost ($) Greek symbols Γ Mass flow rate of working unit per wetted length (kg/ms) ε Heat exchanger efficiency ηII Second law efficiency Mechanical efficiency ηm Electrical efficiency ηel ηis Isentropic efficiency θCO2 Emission conversion factor μ Dynamic viscosity (Pa.s) v Kinematic viscosity (m2/s), ρ Density (kg/m3) ϕ Maintenance cost factor Subscripts abs Absorber cascond Cascade condenser comp Compressor cond Condenser eff Effective evap Evaporator gen Generator in Inlet condition l Liquid out Outlet condition overlap Degree of overlap ref. Refrigerant RHX Regenerative heat exchanger sat Saturation SHX Solution heat exchanger sol,pump Solution pump v Vapor

1 Introduction Absorption cooling systems have been successfully utilized since the era of late nineteenth century and a great deal of effortful improvement have been made on their engineering design and fundamental principles in order to overcome the intrinsic deficiencies in the overall system performance [1]. These type of heat conversion systems have many advantageous features over its counterparts and as a consequence they have been nominated as a possible replacement candidate to vapor compression refrigerators, which is very similar to

traditional absorption refrigeration systems with having a compressor replaced with a generator, pump and absorber. This superiority has been previously mentioned in some of the literature studies [1–4], those discussing some beneficial advantages of these systems such as lower vibration and noise in operation, relatively lower energy consumption and possibility of harnessing low grade waste heat acquired from renewable heat sources with temperatures above 80 °C for cooling purposes. Supplied energy obtained from the industrial waste heat and solar collectors are favourable options for heat generation, however full and effective utilization may not be accomplished if they are not implemented properly. Apart from these advantageous features, some disadvantages of absorption systems are lower overall cooling performance and relatively higher investment cost compared to vapor compression systems. Among available working fluid pairs used in absoprtion cooling systems, LiBr-H2O is the most preffered one as it has a higher latent heat of vaporization and lower toxicity than the other working fluid solutions. However, a system using LiBr-H2O as a working fluid may not be practical in some cases due to the limitations in evaporator temperatures since the water used as refrigerant in the evaporator can not be utilized at working temperatures below 0 °C [5]. Absorption refrigeration systems have undergone a serious development over years in terms of enhancing heat recovery capabilities, which results in providing more efficient design options to conquer some system-related drawbacks. Coupling of absoption coolers with conventional vapor compression systems is one of the major contribution to possible system design alternatives, which considerably reduces the total electricity consumption to acceptable levels by means of reducing condenser temperatures, and thereby cuts down on the emission of pollutant gases to atmosphere. Application of such hybrid cascade systems therefore not only saves a huge amount of electrical energy but also prevents highly toxic greenhouse-causing gases from the environment. Cascaded Vapor Compression Absorption Refrigeration System (CVCARS) concurrently benefits from the available heat and electrical energy during its operation as its full utilization cloak the defficiencies of both Vapor Absorption Refrigeration System (VARS) and Vapor Compression Refrigeration System (VCRS) [6]. Some superior attributes of CVCARS over VARS can also be given such that it has reduced environmental impact and lower energy expenditures compared to single stage absorption cooling system. Required compression power in VCRS is supplied from the shaft work obtained from turbine or gas engine while heat generation in VARS is maintained by the low grade waste heat obtained from industrial applications or solar resources [7]. Plenty of research studies are available in the literature regarding the elaborate evaluation of compression –absorption refrigeration cycles. Much of these works are based on theoretical analysis and limited experimental research studies have been made concerning the evaluation of the effectiveness of

Heat Mass Transfer

absorption-compression type refrigeration cycles. Goktun and Er [8] carried out an energy optimization analysis on a cascade vapor compression absorption system comprising a vapor compression cycle at lower temperature side and a solarassisted absorption refrigerator. Optimal solar collector temperatures are derived in order to obtain maximum COP values. Kaoirouani and Nehdi [9] conducted theoretical thermodynamical analysis on a cascade vapor compression absorption system whose energy supply is maintained by a geothermal water. Selected working fluids including R717, R22, and R134a are used in vapor compression cycle while ammoniawater pair is utilized in absorption cycle. Numerical results obtained from theoretical analysis revelaed that COP of the cascade system is considerably higher than that of the single absoption refrigeration system. It was also shown that refrigeration capability of R717 is superior to the other compared refrigerators under the same operating conditions. Sun [10] set up an experimental rig built on an integrated refrigeration cycle incorporating a gas engine, vapor compression refrigerator and absorption refrigerator. Vapor compression cyle is run by the input work supplied by the gas engine while the waste heat of the engine operates the vapor absorption system. Performance of the refrigeration system is evaluated in terms of primary energy ratio and its corresponding coefficient of performance rate. Outcomes of the experimetal evaluations reveal that primary enery ratio of the integrarted cycle is greatly decreased with increasing gas engine motor speed, while cooling capacity of the system is enhanced as motor speed increases. Fernandez-Seara et al. [11] investigated the applicability of vapor compression absorption system operated separately with CO2 and NH3 refrigerants in the compression stage and NH3-H2O pair in the absoption stage. A mathematical model is developed to analyse the effects of operating conditions on the cascade system performance. Sachdeva et al. [5] made a second law based analysis on a vapor compression cascade system in which ammonia-water pair is considered as an absorption section working fluid, and R407C is used as a refrigerant in the vapor compression section. Exergy destruction of each cycle component is evaluated and compared for varying cooling capacity rates. Furthermore, Coefficient of Structural Bond (CSB) analysis has been performed in order to investigate the influences of varying cascade system parameters on the cooling performance of the hybrid cascade refrigeration cycle. It is observed that solution heat exchanger and condenser have the highest impact on CSB values, that means they have the highest potential to reduce the total system irreversibility rates. Jain et al. [12] investigated the effectiveness and efficiency of a vapor compression absorption system in terms of a modified GouyStodola equation and corresponding results have been compared with the results obtained from the classical exergy analysis. Mathematical formulations are expressed by means of the effective temperature and exergy calculations have been

performed based on this temperature value. Parametric analysis on design variables show that increasing generator and evaporator temperature and decreasing condenser,absorber, and cascade condenser temperatures leads to a signifcant improvements on the overall system performance. Jain et al. [13] extends the comparative analysis made on the vapor compression-absorption system by determining an optimum cascade condenser temperature using modified Gouy-Stodola equation, which eventually leads the refrigeration capacity of the cascade system towards better levels of cooling rates. Obtaining optimum cascade temperature gives rise to the overall COP rates while causing a marked decrease in total irreversibility rate of the cascade system. Most of the earlier literature studies dealing with the performance evaluation of CVCARS are primitive to some extent as the whole refrigeration system was solely investigated based on the first law of thermodynamics, whereas the second law effects have not been taken into account. Efficacy of any energy conversion system is more reliably and completely analyzed with considering the influences of the irreversibilites on the system performance along with the thermodynamic investigations built upon the aspects of the first law. It is also noteworthy to mention that structural complexity of a cascade absorption compression cycle is very high due to the large number of heat exchangers incorporated into the refrigeration system. Capital cost of the CVCARS increases with increasing number of cycle components, which makes the implementation of the integrated cycle system process more challenging and tedious than the conventional refrigeration systems. Jain et al. [14] discussed this issue in their study based on comparative performance analysis and reported that predicted investment cost of the CVCARS is 3.6 times higher than that of the equivalent VCRS. Therefore, it should be one of the utmost concerns of a designer to reduce the total cost by applying an optimization strategy to a refrigeration system. Previous researchers dealing with this issue used various optimization methods to minimise total cost consisting of investment and operational costs. Direct Search Optimization method was successfully applied to thermoeconomic design of a CVCARS by Cimsit et al. [15] and Jain et al. [16] and they reported a significant cost savings. Although these studies give tangible insights on thermoeonomic modelling of these type of refrigeration systems, mere consideration of the economic aspects may lead to unfeasible design points at which environmental concerns and second law effects are somewhat disregarded [6, 17]. This may result in a refrigeration system with releasing high level of pollutant emissions or without taking into account of second law considerations. Exergetic analysis should be elaborately made and low carbon emission technologies should be improved and promoted in order to develop energy efficient and environmental friendly refrigeration systems. Therefore, it can be concluded that an effective CVCRAS should satisfy all the aspects of environmental,

Heat Mass Transfer

economical and exergy issues. However, inherent conflicting nature of these design objectives necessitate the application of multi objective optimization on the related refrigeration system. There are many research approaches in literature that discuss the multi objective optimization of different types of thermodynamic cycles [18–23] and heat exchangers [24–28]. In addition, there are several accomplished research studies concerning the multiobjective design of an absorption refrigeration cycle. Gebreslassie et al. [3] proposed a mathematical programming based optimization procedure to design an environmentally and economically conscious absorption refrigeration system. Jain et al. [6] considered two design objectives including total product cost and total irreversibility for multiobjective design optimization of 170 kW vapor compression absorption cycle. Comparative investigation results showed that thermodynamical analysis of the cascade refrigeration system is more deeply and thoroughly explained by means of multi objective design considerations rather than individually optimized design objectives. This research study discuss the multi objective design optimization of CVCARS considering two different problem objectives. Second law efficiency is taken as a design objective that accounts for the thermodynamic considerations while total product cost is another problem objective concerning the economical aspects of the refrigeration system which includes the capital cost and maintenance cost of the system components and social enviormental costs burdened by CO 2 emmissions. These design objectives are simultaneously and individually applied to CVCARS by virtue of Artificial Cooperative Search [29] metaheuristic optimization algorithm to achieve the optimal design points of the abovementioned vapor compression absoption refrigeration cycle. To the authors’ best knowledge and experience on the literature works dealing with the application of CVCARS, performance analysis of these type of refrigeration systems have not been comparatively investigated, that is, each research study devoted to analyse the thermodynamic and economic aspects of the CVCARS only considers the analysis of a single refrigerant in vapor compression stage, disregarding the comparative investigation between other working fluids with regard to cost analysis and thermodyanmical efficiencies. This study aims to investigate the application and effectivity of CVCARS operated with four different working fluids in the vapor compression stage. Efficiency and applicability of the CVCARS working separately with R134a, R1234yf, R717, and R290 refrigerants are comparatively investigated and best cycle configuration is selected based on the numerical results obtained from single and multi objective optimization analysis. Another aim of this study is to construct Pareto curve for each cycle configuration to provide better solution alternatives to designers. Best result of the non-dominated Pareto solutions retained from multi objective optimization analysis is chosen by the renowned TOPSIS decision making method and parametric

analysis is performed based on the best answer acquired by TOPSIS method for each cycle configuration.

2 Fundamentals of a basic absoption-compression refrigeration system 2.1 Brief description of the CVCARS Figure 1 shows the schematic diagram of a simple aborptioncompression refrigeration system using a regenerative heat exchanger between condenser and cascade condenser to utilize the available relatively high grade energy. Cascade cycle shown in Fig. 1 includes two seperate refrigeration system including vapor compression circuit at low-temperature cycle and absoption refrigeration circuit at high temperature cycle. Absoption cycle uses LiBr-H2O solution as a working fluid while vapor compression cycle uses various refrigerants such as R134a, R1234yf, R717, and R290 in this study to comparatively investigate the influences of each utilized refrigerant on design objectives. Most of the literature studies regarding to thermal design of CVCARS used LiBr-H2O in the absorption stage because of its satisfactory thermal capabilities [14, 16, 20, 30–33], however several research studies have been made using NH3-H2O as a working fluid in the absoption stage [11, 34–36]. Cascade condenser builds a bridge between these two refrigeration cycles by acting as an evaporator for absoption refrigeration cycle and condenser for vapor compression cycle. The solution pump in the absorption cycle draws the weak solution from the absorber and pump this weak LiBr-H2O solution to the solution heat exchanger. Cooled LiBr-H2O solution in the solution exchanger arrives to high pressure generator and absorbs the applied heat which entails the removal of the available water in the weak solution. Strong solution leaving the generator passes through the solution heat exchanger releasing a certain amount of heat to cold weak solution side and right after that goes through the expansion valve to depressurize the high pressure solution. Low pressure strong solution enters the absorber section to complete the cycle. Excess heat in the absorber is taken by the cooling water. It is worth to mention that the pump work required to elevate the LiBr-H2O solution to higher pressures is much lower than that of compressor power of the vapor compression cycle as the liquid solution volume is extremely lower compared to that of the refrigerant vapor operated in vapor compression cycle [37, 38]. A regenerative solution heat exchanger is placed between absorber and generator to increase the inlet temperature of the weak solution and decrease the outlet temperature of the strong solution, bringing considerable energy saving to the system. Generator is an essential and important component of the VARS as it is the only heat exchange device in which energy consumption takes place. Low grade heat applied on the weak solution causes

Heat Mass Transfer Fig. 1 Basic schematic diagram of vapor compression-absorption refrigeration cycle

evaporation of the water in the solution. The refrigerant at the exit of the generator is pure water as the salt has no ability to exert any vapor pressure [39]. Water vapor leaving from the generator goes to the condenser, releases heat to the cooling water and becomes saturated liquid at the condenser outlet. Pressure of the saturated liquid stream is reduced by means of the expansion valve and is directed to cascade condenser where vapor compression and absorption refrigeration cycles are linked together. Latent heat absorbed from the condenser section of the vapor compression cycle is applied to saturated liquid in the evaporator to accomplish evaporation. Saturated steam then passes through a regenerative heat exchanger to utilize the available heat at the condenser outlet. Finally, the regenerated steam goes to the absorber and absorbed by the strong solution. Meanwhile in the vapor compression cycle,

the working fluid at the evaporator outlet is compressed to higher pressures by the compressor and directed to the cascade condenser at where the working fluid (refrigerant) goes into a phase change and rejects its inherent latent heat to the evaporator side of the cascade condenser. Overlap temperature in the cascade condenser takes an essential and prominent role in design consideration as it affects the COP values of the cascade refrigeration system [11]. Refrigerant in the form of saturated liquid passes through the expansion valve to reduce the working pressure and enters the evaporator to accomplish the circulation of the working fluid of the vapor compression cycle. This integrated refrigeration cycle comprises various type of heat exchanger units and system components in which phase and temperature changes and pressure drops occur.

Heat Mass Transfer

Therefore, some requisite assumptions should be made not only to simplify and ease the modelling and analysis of the above mentioned CVCARS, but also to decrease the computational load burden caused by the excessive redundant calculations. Cooling tower cost is not included into total cost analysis as the excess heat is rejected to a cooling water which is plenty and does not need further processes [16, 40–42]. It is also assumed that absorbed energy in the generator of the absorption cycle is supplied from an industrial low grade waste heat [12, 16]. Other major simplifications and assumptions made on the system analysis can be listed as below [6, 16, 43–45]: 1- CVCARS system operates under steady state conditions and the state of the refrigerant at the outlet of the condenser, evaporator and cascade condenser is assumed to be saturated. 2- All pressure and heat losses throughout the refrigeration system are neglected and disregarded. 3- Pressure drop process taken place in the expansion valve is assumed to be isenthalpic 4- The weak and strong solution of LiBr-H2O respectively leaving from absorber and generator are considered to be saturated and equilibrium with their corresponding working temperatures and pressures. 5- Influences of the kinetic and potential energies on the thermodynamic analysis are disregarded.

2.2 Thermodynamic modelling of the integrated refrigeration system Based on the above given assumptions and simplifications, thermodynamic modelling of each system component is maintained relying upon the following energy and mass balance equations. Governing equations regarding to mass balance are ˙ ¼ 0; ∑x⋅m˙ ¼ 0 ∑m

ð1Þ

and energy balance is : : : ∑ Q þ ∑ W þ ∑ðm ⋅ hÞ ¼ 0

ð2Þ

These two equations are the main balance equations for each cycle components of CVCARS and applied to obtain the corresponding mass flow rate, the required compressor and pump work, and the rate of heat transfer for different thermodynamic cycle equipments. Table 1 reports the energy and mass balance equations for each cycle component. Isentropic efficiency of the VCRS compressor can be described as a function of hot and cold side working pressures and formulated as below [46].


 Pcond ηis ¼ 1− 0:04  Pevap

ð3Þ

Mechanical (ηm)and electrical (ηel)efficiencies of the VCRS compressor are taken as 0.93 [47]. Thermodynamic and thermophysical properties of each working fluid used in the refrigeration cycle are obtained using CoolProp [48] open source software package. COP of the different cycles of the CVCARS can be formulated as below: : : ð4Þ COPVCRS ¼ Qevap =Wcomp   ˙ ˙ COPVARS ¼ Q˙ cas;cond = Q ð5Þ gen þ W pump   COPCVCARS ¼ Q˙ cas;cond = Q˙ gen þ W˙ comp þ W˙ pump

ð6Þ

Second law efficiency of the cascade system is evaluated based on the expression proposed by Kotas [38], which describes the exergy efficiency of the cascade system as a function of product exergy divided by fuel exergy. In this context, exergy input to the evaporator in the vapor compression side takes the product role while the rate of the exergy change in the generator caused by the supplied low grade energy act as a fuel. Exergy efficiency of the cascade refrigeration system can be expressed below given formulation depending on the above given explanation.   m˙ cool;wat ðh23 −h24 Þ−T eff ;evap ðs23 −s24 Þ   ηII ¼ ˙ ð7Þ mgen;wat ðh19 −h20 Þ−T eff ;gen ðs19 −s20 Þ Where Teff, evap and Teff, genare respectively effective evaporator and generator ambient temperatures obtained by the modified Gouy-Stodola equation. Some literature studies [12–14, 16, 37] asserted the idea that using modified GoutStodola equation is more beneficial compared to its simple form as actual exergy loss rates can only be determined by effectve temperature rather than actual environment temperature. Detailed description and discussions made on the application of simple and modified form of the Gouy-Stodola equation on vapor-compression absorption refrigeration systems were discussed in the above mentioned literature works.

2.3 Economic analysis of the integrated refrigeration system Operational, capital and maintanence costs as well as the social cost due to CO2 emissions are considered for the evaluation of economic analysis of the refrigeration cycle. Operational cost is incurred by the power consumption occurring in the generator, compressor, and pump of the

Heat Mass Transfer Table 1 Energy and mass balance equations for various cycle components

˙ ˙ m˙ 7 ¼ m ref ;VARS þ m12 ˙ ˙ x10 ⋅m12 ¼ x9 ⋅m7 ˙ ˙ Q˙ abs þ m˙ 7 h7 ¼ m ref ;VARS h6 þ m12 h12 ˙ Qabs ¼ mref ;abs ⋅C p;ref ⋅ðT 18 −T 17 Þ m8 ⋅ðP8 −P7 Þ ˙ m˙ 7 ¼ m , 8 ,W pump;sol ¼ ρ⋅ηp ˙ m˙ 7 h7 þ W pump;sol ¼ m h 8 8 ˙ ˙ ˙ m˙ 8 ¼ m 9 ; m10 ¼ m11 ˙ ˙ ˙ ˙ Q˙ sol;hex ¼ m 10 h10 −m11 h11 ¼ m8 h8 −m9 h9 T 10 −T 11 ε ¼ T 10 −T 8 ˙ ˙ m˙ 9 ¼ m ref ;VARS þ m10 ˙ ˙ ˙ Qgen þ m9 h9 ¼ mref ;VARS h13 þ m˙ 10 h10 Q˙ gen ¼ mref ;gen ⋅C p;gen ⋅ðT 19 −T 20 Þ ˙ m˙ 11 ¼ m 12 ; h11 ¼ h12 ˙  ˙ ¼ m ⋅C p cond;ref ðT 21− T 22 Þ Qcond ¼ m˙ ref ;VARS ðh13 −h14 Þ ˙ ˙ ˙ ˙ m˙ ref ;VARS ¼ m 14 ¼ m15 ¼ m5 ¼ m6 ˙ ˙ ˙ ˙ Qreg;HEX ¼ m14 ⋅h14 −m15 ⋅h15 ¼ m˙ 5 ⋅h5 −m 6 ⋅h6 ˙ ˙ m15 ¼ m16 ; h15 ¼ h16 ˙ ˙ Q ¼ mref ;VCRS ðh2 −h3 Þ, cas;cond ¼ mref ;VARS ðh5 −h16 Þ

Absorber

Pump Solution heat exchanger Generator

Expansion valve 2 Condenser Regenerative heat exchanger Expansion valve 3 Cascade condenser

˙ ˙ ˙ ˙ ˙ ˙ m ref ;VARS ¼ m16 ¼ m5 mref ;VCRS ¼ m2 ¼ m3 ˙ ˙ ˙ ˙ m˙ 1 ¼ m 2 ; m1 h1 þ W comp ¼ m2 h2   ˙ Qevap ¼ mref ;VCRS ðh1 −h4 Þ ¼ m⋅C p ref ;evap ðT 23 −T 24 Þ ˙ m˙ 3 ¼ m 4 ; h3 ¼ h4

Compressor Evaporator Expansion valve 1

refrigeration system and can be formulated as the following expression:    ˙ ⋅C C oper ¼ W˙ comp þ W˙ pump ⋅C elec þ Q ð8Þ gen fuel ⋅H Where Celec and Cfuel are respectively unit electrical and fuel cost and considered as 0.075 $/kWh [6, 17] and 0.03785 [6, 40]; and H stands for the total annual operation hours of the refrigeration system and taken as H = 5000 h [6]. Capital cost of each heat exchange unit along with the compressor devices are taken into overall cost considerations, while neglecting the cost effects of the expansion valves, refrigerant piping and refrigerants as they constitute very small portion of total cost of the system. A cascaded vapor compression absorption refrigeration system is composed of various type of heat exchangers including an absorber, generator, condenser, evaporator, cascade condenser, in addition to auxiliary heat exchangers such as solution heat exchanger and regenerative heat exchanger which are optional to use and beneficial for energy saving purposes. Investment cost of each heat exchange unit is calculated by the folowing formulation [6]. Z i ¼ 516:621⋅Ai þ 268:45

ð9Þ

Where Zi and Ai respectively represent capital cost and heat exchange area of each heat exchanger. Investment cost of the

low temperature vapor compression cycle compressor is obtained by the below given formulation


 573m˙ ref ;VCRS Pcond Pcond Z comp ¼ ln ð10Þ 0:8996−ηis Pevap Pevap Total investment cost of the system can be expressed by the below given formulation C inv ¼ ϕ⋅CRF⋅∑Z i

ð11Þ

Where ϕis the maintenance cost factor and taken as 1.06 [6, 23]. Capital recovery factor is denoted by CRF and expressed by the following formulation CRF ¼

ið1 þ iÞN ð1 þ iÞN −1

ð12Þ

Where N and i are respectively life time of the refrigeration system and interest rate. Numerical values of these parameters are correspondingly considered as N = 10 [6] and i = 0.1 [6]. Increasing global warming threats and observed increases in ozone depletion rates have urged designers and researchers associated with power generation industries to find environmentally friendly solutions to this serious problem. These researchers and designers are aware of the issue that consumption of the fossil fuels for generating electricity takes the major

Heat Mass Transfer

role in the excessive release of CO2 emissions. Therefore, main aim for them has been for years to find promising design alternatives for reducing pollutant and hazardous CO2 emissions. Carbon pricing method covers several ways of putting market price on an emission of any carbon-based gases extracted from fossil fuel. Among the differernt options for reducing carbon emissisons by means of carbon pricing based strategies, carbon tax becomes the leading procedure and is applied in ways to tackle with global warming issues. Carbon tax method is simple and based on the procedure such that the more you burn fossil fuel, the more you have to pay taxes. A suitable and simplified mathematical formulation designed for estimating the amount of carbon tax charge is expressed by the following equation C env ¼ mCO2 C CO2

ð13Þ

compression cycle are modelled as shell and tube heat exchanger in which cooling water is used as secondary fluid, whereas solution heat exchanger and regenerative heat exchanger are designed as double pipe heat exchanger. Copper tubes are used for piping for each heat exchanger [1, 6]. Table 2 reports the heat transfer calculation procedure for each flow stream taken place in the refrigeration system. Tables 3 and 4 show the structural characteristics of different types of heat exchangers operated in the CVCARS. Heat exchange surface area of each heat exchnager for the given imposed heat load is computed by the following expression A¼

˙ Q U ΔT LMTD

ð16Þ

Where C CO2 is the penalty cost for the emission of pollutant carbon dioxide. Though social cost of the carbon emsission is depended upon the legislative actions of the related government department, this study considers this penalized cost value as $90 per ton of CO2 emission [49]. Numerical value of the mCO2 in Eq. (13) is calculated by

Where A is the required heat exchange surface to maintain heat transfer between two streams; ΔTLMTD is logartihmic mean temperature difference and its relevant calculation for each heat exchange device is given in Table 5; and U is the overall heat transfer coefficient based on the tube outer surface and computed by the following

mCO2 ¼ θCO2 ⋅W˙ comp ⋅H

U ¼ 


ð14Þ

Where W˙ comp represents the energy consumption incurred by the compressor; and θCO2 is the emission conversion factor of electricity from grid and taken as 0.968 kg kWh−1 [50]. In the light of the above given explanations and descriptions, total annual cost of the integrated cascade refigeration system becomes the summation of the operational, investment and social cost resulting from carbon emissions and summed up in one equation given below C T ¼ C oper þ C inv þ C env

ð15Þ

2.4 Heat exchanger modelling and design As it is explained and discussed in above section, heat exchange surface area plays dominant role in determining the investment cost of the refrigeration system. Therefore, thermal design and modelling of each individual heat exchnager unit taken place in the refrigreation system should be carefully made and utmost concern should be given to proper usage of the correct heat transfer correlation. Two phase heat transfer occurs in condenser, evaporator, and cascade condenser. Absorber, generator, condenser, cascade condenser, and evaporator in the vapor

d out d in




1 hin




þ

1

 
 ð17Þ d out d out d out 1 ln Rin þ þ Rout þ d in 2k d in hout

Eq (16) is applied to each heat exchanger and its corresponding heat exchange area is used for calculating the related investment cost.

2.5 Validation and verification of the proposed themodynamic cycle model As there are no available reliable experimental data associated with the thermal design of CVCARS in the open literature, accuracy of the proposed thermodynamic model in this study is validated against the numerical outcomes of the some of the well established former literature approaches dealing with theoretical efficiency investigation of these kind of refrigeration systems. Results of the theoretical models obtained from the literature works used for the accuracy validation of the above explained thermodynamical design model, along with the corresponding percentage error values are given in Table 6. These past modelling approaches include the theoretical performance investigation studies of Cimsit and Ozturk [43], Jain et al. [12], and Jain et al. [16]. Cimsit and Ozturk [43] presented a comparative investigation study about thermal design issues related to using different working fluids in the compression and absorption section of the cascaded refrigeration system. Operating conditions which are used to produce theoretical data for R134a refrigerant for comparison are: Tevap =

Heat Mass Transfer Table 2

Heat transfer coefficient calculation method for each stream in the CVCARS

Correlation

Description

Formulation

Gnielinski [51]

Used for single phase heat transfer taking place evaporator, condenser, absorber, gerenerator, and regenerative heat exchanger

vm ¼ 

Incorpera and Dewitt [52]

Designed for the tube outside condensation occured in the condenser. Applicable to laminar flows Used for calculating external heat transfer coefficient at the generator Used for calculation of internal heat transfer coefficient in the cascade condenser.

Bakhtari et al. [1] Chato [53]

Song [54] Hoffmann et al. [55] Florides et al. [4]

For calculation of falling film evaporator heat transfer coefficient Used to compute the falling film heat transfer coefficient in the absorber Equations for calculating heat transfer coefficients for hot and cold sides in the solutionheat exchanger

261 K, Tabs = 313 K, Tgen = 363 K, Tcond = 313 K, Toverlap = 8 K, εSHX = 0.60 and with the imposed cooling load of Qevap = 50 kW. It is seen that maximum absolute percentage error between the literature data and proposed model results is about %0.9. Another modelling study made by Jain et al. [12] is concerned with the energy and exergy performance investigation of a CVCARS with using the modified Gouy-Stodola equation rather conventional exergy calculation principles. LiBr/H2O working fluid is used in the absorption cycle while R22 refrigerant circulating through the low temperature vapor compression cycle circuit. Design conditions of the mentioned refrigeration system can be summarized as follows: Tevap = 272.6 K, Tabs = 313 K, T gen = 363 K, Tcond = 318.2 K, ˙ Toverlap = 8.0 K, εSHX = 0.60, m ref ;VCRS ¼ 0.4432 kg/s, ˙ ˙ mref ;VARS ¼ 0.5064 kg/s, and Qevap ¼ 80.7 kW. Simulation model proposed in this study is modified in accordance with Table 3 Dimensional parameters of the various type of heat exchangers in the CVCARS Shell diameter (m) Baffle spacing (m) Tube outer diameter (m) Tube inner diameter (m) Number of tube pass Tube pitch (m) Fouling factor (m2K/W) Tube configuration

˙

C μ m=ρ Re ¼ ρvμm d Pr ¼ kp 2 0:25πd ð in Þ  f Pr ffi k pffiffiffiffiffi h ¼ 8 ðRe−1000Þ 0:666 −1Þ d in 1:0þ12:7 f =8ðPr f = (0.79 ln(Re) − 1.64)−2  0:25 ρ ðρ −ρ Þg⋅hfg ⋅k 3 h ¼ 0:729 μ l⋅doutl ⋅ðTg sat −T walllÞ N −0:25 t;bundle N tube N pass

l

h = 5554.3Γ0.236  0:25 0 g⋅ρ ðρl −ρv Þ⋅k 3l ⋅hfg h ¼ 0:555 μ ⋅lðT sat −T wall Þ⋅d l

0

hfg ¼ hfg þ 0:375C p;l ðT sat −T wall Þ
 0:5 l h ¼ 0:177 Pr2 ⋅k1=3 ν =gÞ  ð l−1:7 h ¼ 2000 10ν−6l dH = dout − din  For annulus flow: ˙ ⋅d 3:66⋅k=d H ←if ðReH < 2300Þ H ReH ¼ mA⋅μ h← Apply Gneilinski equation←else  For intube flow: ˙ 3:66⋅k=d in ←if ðRein < 2300Þ 4:0m Rein ¼ πdin μ h← l Apply Gneilinski equation←else

the above given operational conditions and it is observed that predicted results are in good agreement with the theoretical data as maximum absolute percentage error between them is about within 1.4%. Numerical results retained from the integrated cascaded vapor compression absorption system of Jain et al. [16] are compared with the model results in Table 6. Input design data used for comparison can be listed as: Tevap = 273.15 K, Tabs = 313 K, Tgen = 358 K, Tcond = 313 K, ˙ ˙ Toverlap = 8.0 K, εSHX = 0.60, m ref ;VCRS ¼ 0.415 kg/s, mref ;VARS ˙ ¼ 0.037 kg/s, and Qevap ¼ 80.7 kW. Reported results given in Table 6 show the prediction accuracy of the proposed model is quite satisfactory such that maximum error deviation is around −2.0%. Figure 2 shows the comparison between the acquired model results and benchmark data obtained from Jain et al. [16] regarding to total operational cost and irreversibility rates, accompanied with the corresponding relative error values.

Condenser

Evaporator

Generator

Absorber

Cascade condenser

0.3 0.2 0.016 0.0128 2.0 0.02 0.000044 Triangular

0.3 0.2 0.02 0.016 2.0 0.025 0.000044 Triangular

0.3 0.2 0.02 0.016 1.0 0.025 0.000044 Triangular

0.3 0.2 0.02 0.016 1.0 0.025 0.000044 Triangular

0.4 0.2 0.02 0.016 2.0 0.025 0.000044 Triangular

Heat Mass Transfer Table 4 Specifications of the double pipe solution heat exchanger and regenerative heat exchanger Solution heat exchanger

Regenerative heat exchanger

Outer tube diameter (m)

0.035

0.020

Thickness of outer tube diameter (m)

0.005

0.004

Inner tube diameter (m) Thickness of inner tube diameter (m)

0.025 0.004

0.012 0.002

Relatively negligible error values are observed for two comparison cases for each temperature state. Figure 3 shows the variation of the error values with increassing evaporator working temperatures based on the data taken from Cimsit and Ozturk [43]. It is seen that predicted results are in line with the theoretical data and deviation rates are not more than 0.8% for each comparison case.

3 Multi objective optimization Engineers and designers have generally found themselves in solving hard-to-solve multi-task design problems which contain many conflicting design objectives those should be simultaneously satisfied. These type of problems have numerous possible alternative solutions which are non-dominated to each other and trade-off between the contradictory design objectives. Any improvement made on one objective cause a jeopardization on other problem objectives or vice versa. In this situation, it is not possible to assert the claim that one solution is better than the other by evaluating the quality of Table 5 Logarithmic mean temperature difference calculation procedure for each heat exchange device in the refrigeration system Component

ΔTLMTD

Absorber

 18 Þ−ðT 7 −T  17 Þ ΔT LMTD;abs ¼ ðT 12 −T T −T ln

Generator

10 Þ−ðT 20 −T  13 Þ ΔT LMTD;gen ¼ ðT 19 −T T −T ln

Condenser

ðT 10 −T 9 Þ ðT 11 −T 8 Þ

−T 5 Þ  6 Þ−ðT 15 ΔT LMTD;RHX ¼ ðT 14 −T T −T ln

Evaporator

ð 22 13 Þ ðT 21 −T 13 Þ

ΔTLMTD, cascond = T3 − T5 −T 8 Þ  9 Þ−ðT 11 ΔT LMTD;SHX ¼ ðT 10 −T ln

Regenerative heat exchanger

ð 19 10 Þ ðT 20 −T 13 Þ

13 Þ−ðT 21 −T  13 Þ ΔT LMTD;cond ¼ ðT 22 −T T −T ln

Cascade condenser Solution heat exchanger

ð 12 18 Þ ðT 7 −T 17 Þ

ð 14 6 Þ ðT 15 −T 5 Þ

−T 4 Þ  4 Þ−ðT 24 ΔT LMTD;evap ¼ ðT 23 −T T −T ln

ð 23 4 Þ ðT 24 −T 4 Þ

its corresponding fitness value, as it happens in the single objective optimization. Therefore, we can conclude that single objective optimization aims to obtain the global best answer among the plenty of numerous alternatives while multi objective optimization deals with finding set of solutions in which no superior or inferior solution takes place between them. These non dominated solutions are called BPareto solutions^ forming the Pareto curve. There are also ideal and nadir points taking place outside of the curve, which respectively represent best and worst solution of the problem obtained in the manner of single objective optimization. Artificial Cooperative Search (ACS) metaheuristic algorithm is applied to each thermodynamic cycle design case in this study for simultaneous and individual optimization of the two design objectives including second law efficiency and total annual cost of the CVCARS. ACS is a nature inspired swarm intelligence based metaheuristic optimization algorithm which is efficient and dexterous in solving multi dimensional optimization problems, thanks to its excellent maintained balance between exploration and exploitation phases. Attained harmony between these well-balanced phases not only increases the solution accuracy and efficiency but also eliminates the premature convergence, which is an undesired process leading to stuck in local optimum points in the search domain. Algorithm is built on the migration and food searching strategies of two independent superorganisms on the course of finding the best habitat for their sufficient subsistence. This natural phenomenon is mathematically converted into a set of algorithmic procedure and forms the ACS algorithm. Detailed explanation and description about the subalgorithms constituting the whole ACS method are not given in this study due to limited space restrictions, however interested readers can refer to its original paper [29] and could find more about its fundamental algorithmic construction in this reference. There is only one multiobjective optimization application of ACS algorithm in the open literature, in which multi objective economic-emission disptach problem is solved [56]. Therefore, we can deduce that its optimization performance in multi objective design problems has not been accurately and reliably verified yet. This study also aims to fill another gap on assessing the optimization performance of ACS algorithm over multi dimensional highly non-linear real world design problems and also to give tangible outcomes to the readers on its success over Pareto curve construction. A conventional multi-objective optimization problem can be defined by the below expression   Min=max f i ! x i ¼ 1; 2; …; N   x ≤0 subject to g j ! j ¼ 1; 2; …; M ð18Þ   ! k ¼ 1; 2; …; K hk x ¼ 0 xLm ≤ xm ≤ xU m

m ¼ 1; 2; …; P

Heat Mass Transfer Table 6

Validity check of the proposed model of CVCARS against the outcomes of the various literature works

˙ Q abs ˙ Q gen ˙ Q cond ˙ Q evap ˙ Q cas;cond W˙ comp COPCVCRAS COPVCRS COPVARS

Ref. [43]

Model

Error (%)

Ref. [12]

Model

Error (%)

Ref [16]

Model

Error (%)

72.46 76.45 61.06 50.00 57.41 8.250 0.590 6.061 0.750

72.79 76.33 61.38 50.31 56.98 8.338 0.594 6.033 0.746

0.4 −0.1 0.5 0.6 −0.7 0.9 0.6 −0.4 −0.5

121.20 126.90 95.71 80.80 89.95 9.25 0.592 8.723 0.708

121.74 126.38 96.47 81.23 90.76 9.37 0.598 8.664 0.718

0.4 −0.4 0.7 0.5 0.9 1.3 1.0 −0.6 1.4

114.94 120.20 93.69 80.70 88.43 9.16 0.630 10.430 0.735

115.56 120.76 94.01 80.31 88.00 8.97 0.623 10.491 0.728

0.5 0.4 0.3 −0.4 −0.4 −2.0 −1.1 0.5 −0.9

In above equations, ! x represents the set of P dimensional decision variables in the form of: ! x ¼ ½x1 ; x2 ; …; xP 

ð19Þ

Upper and lower bound of each design variable are respec! L tively denoted by xU m and xm ; f i x stands for N optimizaton objectives which can also be expressed in the following equation form:  i   h     x ; f2 ! x ; …; f N ! x f ! x ¼ f1 ! ð20Þ     Finally, g ! x and h ! x respectively symbolize M and K number of inequality and equality design constraints imposed on the optimization problem. One another important point in multi objective optimizatiton is that using proper decision making theorem to choose the final best answer among the set of non-dominated solutions in the

Pareto curve. This study considers the well-known and well-reputed TOPSIS decision making method along with applying Euclidian approach for non-dimensionalization. Elaborate description and further useful comments on TOPSIS method are explicity given in the work of Kumar et al. [57]. Decision variables of an optimization problem decide the inclination of the the objective function towards minimum or maximum. Therefore, upper and lower bound of each decision variable should be properly assigned in order to ensure successfull optimization process. Seven design variables are considered including absorber temperature (Tabs), generator temperature (Tgen), condenser temperature (Tcond), evaporation temperature in the cascade condenser (Tcas,cond), and evaporator temperature in the vapor compression cycle (Tevap) and heat transfer efficiency of the solution heat exchanger (εSHX). Their corresponding allowable bounds are given in Table 7.

Fig. 2 Assessing the prediction performance of the proposed model by means of data taken from Jain et al. [16]

Heat Mass Transfer

Fig. 3 Validation of the estimation capability of the proposed model using the theoretical data of Cimsit and Ozturk [43]

Optimization objectives, design variables and problem consraints are three main elements of any optimization desing problem and all three of them should be clearly defined and identified to obtain sucessfull solution of the optimization problem. We have discussed and given explanatory insights on the assignment of decison variables and problem constraints however have not talked much about as to why these design objectives are considered for single and multi objective design optimization purposes. In thermal design of refrigeration system, the prior aim is to model an efficient cycle design which can be accomplished by increasing COP values as high as possible. This increase induce an enhancement in exergy effiency rates, and consequently increase the investment cost of the various equipments of the related thermodynamic cycle. In this context, more than one objective function is needed for reliable optimization of the refrigeration system both taking into account of overall cost and exergy issues. Therefore, this study considers total annual cost (as given in Eq. (15)) and second law efficiency (given in Eq.7) of the CVCARS as two conflicting but complementary design objectives those should be concurrently and individually solved to obtain the global Table 7

Upper and lower bounds of optimization variables Lower bound

Tabs (°C) Tgen (°C) Tcond (°C) Tcas,cond (°C) Tevap (°C) Toverlap (°C) εSHX

15.0 95.0 60.0 6.0 −20.0 6.0 0.6

Upper bound 25.0 105.0 70.0 15.0 −10.0 15.0 0.9

best answer of the problem. Three objective optimization cases will be investigated covering single objective optimization of total annual cost and second law efficiency as well as multi objective optimization of the CVCARS for each four refrigerant operating in the vapor compression cycle.

4 Optimization results and sensitivity analysis 4.1 Single and multi objective optimization results of CVCARS working with different refrigerants in VCRS Simulation program developed in Java is used to model and optimize the integrated cascaded refrigration cycle. Thermophysical and thermodynamical properties of the working fluids are obtained from CoolProp environment. Due to the stochastic nature of the metaheuristic optimization algorithms, more than one algorithm run is needed to ensure the validity of the attained solution. ACS is run twenty times with 50,000 function evaluations and best result between the obtained solutions is taken and included into the Pareto solutions. Computer codes are run at a desktop computer with quad core Intel i5–4460 CPU @ 3.20 GHz with 16.0 GB RAM. Table 8 reports the single and multi objective optimization results of the CVCARS working with R1234yf in vapor compression cycle. It is seen that optimal total annual cost value is 10,865.74 $/year while second law efficiency for this optimization case is 0.226. When exergy efficiency of the system is individually maximized, its optimized value becomes 0.348 as its corresponding total annual cost reaches to 14,188.363 $/year. The amount of heat transfer rate in the evaporator, condenser, and cascade condenser are increased

Heat Mass Transfer Table 8 Optimal results for the CVCARS operated with R1234yf in vapor compression cycle Minimum total annual cost Tabs (°C) Tgen (°C) Tcond (°C) Tcas, cond (°C) Toverlap (°C) Tevap (°C) εSHX ˙ Q cond (kW) ˙ Qcas;cond (kW) ˙ Q abs (kW) ˙ Q gen (kW) ˙ Q evap (kW) ˙ Q SHX (kW) ˙ QRHX (kW) W˙ sol;pump (kW) W˙ comp (kW) Acond (m2) Acas, cond(m2) Aabs(m2) Agen(m2) Aevap(m2) ASHX(m2) ARHX(m2) COPVCRS COPVARS COPCVCRAS ˙ m CO2 (ton/year) Cenv ($/year) ηII CT ($/year)

Maximum second law efficiency

Multi-objective optimization

24.998 95.005 64.999 6.004 2.871 −10.001 0.703 14.594 14.860

24.996 95.000 64.010 6.003 2.000 −10.000 0.899 18.103 18.434

24.993 95.002 64.999 6.000 2.770 −10.000 0.706 15.100 14.847

22.561 22.812 11.930 15.660 0.405 0.002 3.156 8.998 4.886 14.435 2.251 4.008 5.729 0.529 3.785 0.651 0.459 15.252

22.162 22.474 14.967 19.587 0.490 0.002 3.728 9.705 8.054 29.348 2.653 5.059 17.623 0.761 4.014 0.820 0.571 18.046

22.482 22.733 11.932 15.725 0.405 0.002 3.134 8.985 4.958 14.487 2.250 4.009 5.808 0.427 3.807 0.653 0.461 15.169

1372.700 0.226 10,865.74

1624.183 0.348 14,188.363

1365.25 0.228 10,886.443

in the case of second law efficiency optimization compared to annual cost based optimization results. Heat transfer rates for each remaining heat exchange device in the cycle do not show any significant change. When looking at the variations of the design variables, it is observed that nearly similar decision variable values are obtained for different optimization cases, except for the design variables of overlap temperature and efficiency of the solution heat exchanger. Variations of the solution heat exchanger efficiency values play more dominant role than the influences of the overlap temperature on objective function values because variational changes in the solution heat exchanger exit temperatures (temperature state 11 in Fig. 1) occurred by variations in solution heat exchanger efficiency not only directly affects the overall heat transfer coefficient value of itself but also of the absorber and consequently influences the amount of heat exchange area of both heat

exchnage device in the cycle. As it is expressively mentioned in the former section dealing with economic modelling of the cycle, investment cost of the cycle is directly influenced by the increases or decreases of heat exchange surface areas in the heat exchange equipments. Therefore, based on these above explanations, we can deduce that solution heat exchanger efficiency has a substantial effect on total annual cost. Figure 4 shows the Pareto curve for dual objective optimization of the cascaded refrigeration cycle operated with R1234yf as well as the best pareto optimal solution obtained by TOPSIS decision making method. Optimal solutions of second law efficiency and total annual cost are respectively 10,886.443 ($/year) and 0.228 according to the TOPSIS results. It can be also clearly observed that best answer chosen by TOPSIS is inclined to minimum total annual cost and second law efficiency (lower left side) rather than the opposite side (upper right side). Table 9 lists the optimal results of the single and multi optimization of the CVCARS working with R134 refrigerant in VCRS. Above discussed CVCARS running with R1234yf is considered as base case for performance comparison of the contended integrated refrigeration cycles working with various refrigerants hereafter in this study. Obtained results for this case reveal that total annual cost of the system is decreased by 5.62% and second law efficiency is increased by 9.2% when these design objectives are individually optimized. It is also seen that tendencies of the decision variables are quite similar with those of the base case. Maximum COPCVCARS value when second law efficiency is optimized is 0.622, which is 8.93% higher than that of the base case. Variations in the heat exchange surface areas of cascade condener, absorber, evaporator and solution heat exchanger again become commanding design parameters as it happens in the former case and creates a trade-off between design objectives. Another issue causing an increase in total overall cost

Fig. 4 Pareto curve for the integrated refrigeration system working with R1234yf in the vapor compression cycle

Heat Mass Transfer Table 9 Optimal results for the cascaded refigeration system working with R134a in VCRS Minimum total annual cost Tabs (°C) Tgen (°C) Tcond (°C) Tcas, cond (°C) Toverlap (°C) Tevap (°C) εSHX ˙ Q cond (kW) ˙ Qcas;cond (kW) ˙ Q abs (kW) ˙ Q gen (kW) ˙ Q evap (kW) ˙ Q SHX (kW) ˙ QRHX (kW) W˙ sol;pump (kW) W˙ comp (kW) Acond (m2) Acas, cond(m2) Aabs(m2) Agen(m2) Aevap(m2) ASHX(m2) ARHX(m2) COPVCRS COPVARS COPCVCRAS ˙ m CO2 (ton/year) Cenv ($/year) ηII CT ($/year)

Maximum second law efficiency

Multi-objective optimization

24.998 95.000 65.000 6.000 2.820 −10.043 0.700 14.551 14.817

24.993 95.000 63.890 6.004 2.005 −10.000 0.899 18.684 19.025

24.998 95.000 64.999 6.000 2.663 −10.000 0.749 15.076 14.823

22.558 22.830 12.551 15.596 0.404 0.002 2.437 8.978 4.205 14.336 2.253 4.181 5.642 0.427 5.148 0.648 0.496 11.797

22.800 23.122 16.254 19.519 0.503 0.002 2.979 9.811 7.188 30.353 2.737 5.456 17.478 0.545 5.454 0.822 0.622 14.423

21.504 21.754 12.581 16.678 0.404 0.002 2.411 8.981 4.413 15.542 2.223 4.191 7.140 0.428 5.217 0.681 0.520 11.669

1061.812 0.246 10,254.871

1298.072 0.380 13,753.495

1050.289 0.273 10,285.923

is the environmental cost incurred due to release of the carbon dioxide. Environmental cost of this cycle is 22.7% lower than that of the base study. This is resulted from lower needed compression work of VCRS, which directly affects the amount of carbon emission as it is mentioned in Eq. (14). Figure 5 visualizes the set of non dominated solutions in the form of Pareto curve for CVCARS operated with R134a in VCRS along with the best answer retained by TOPSIS method. Opeating condtions found by TOPSIS method are also reported in Table 9. According to the preferences of mentioned decision making method, best Pareto optimal solution of total annual cost and exergy efficiency of the cascaded refrigeration system are respectively 10,285.92 ($/year) and 0.2739. Table 10 gives the optimal single and multi objective design of the CVCARS operated with R290 in VCRS. Optimal

Fig. 5 Pareto optimal solutions for CVCARS working with R134a in VCRS

annual cost of the system is decreased by 11.8% compared to that obtained in the base study. Apart from that, second law efficiency has improved by 18.6%. As compared with base case study, reduction in total cost is mainly caused by the decreases in the required compressor shaft work (43.3%) directly influencing electricity cost rates, rather than the observed small decreases (2.3%) in total heat exchange surface area of all heat exchange equipments. It is also worth to mention that reduction in the compressor work entails a considerable decrease (43.2%) in social cost related to carbon emissions, which is another factor causing a reduction in total annual cost. Improvement in exergy efficiency values are mainly because of the favourable thermophysical and thermodynamical properties of the propane. They also affect the improvement in COPCVCARS rates (18.5%) when second law efficiency is individually minimized. Inclinations of the decision variables are again similar with those observed in the base case study. Figure 6 shows the pareto optimal results for the cascaded system operated with R290 in the low temperature VCRS and the final answer chosen by.TOPSIS method which is also available in Table 10. According to the best comprimising result obtained by TOPSIS decision making theory, total annual cost and second law efficiency are respectively 9658.271 ($/year) and 0.273. It is found that optimal values of total annual cost is lower, and second law efficiency is higher than those found as comprising result in the base case stıdy. Table 11 reports the single and multi objective optimization results dealing with optimum thermodynamical design of CVCARS running R717 in VCRS. Optimum total annual cost is found to be 9640.37 ($/year), which is 11.2% lower than that found in the base study. Moreover, optimal exergy efficiency obtained from single objective optimization is 0.397, which is 14.0% higher than that found in the base study. One

Heat Mass Transfer Table 10 Single and multi objective optimization results of the CVCARS system operated with propane in VCRS Minimum total annual cost Tabs (°C) Tgen (°C) Tcond (°C) Tcas, cond (°C) Toverlap (°C) Tevap (°C) εSHX ˙ Q cond (kW) ˙ Qcas;cond (kW) ˙ Q abs (kW) ˙ Q gen (kW) ˙ Q evap (kW) ˙ Q SHX (kW) ˙ QRHX (kW) W˙ sol;pump (kW) W˙ comp (kW) Acond (m2) Acas, cond(m2) Aabs(m2) Agen(m2) Aevap(m2) ASHX(m2) ARHX(m2) COPVCRS COPVARS COPCVCRAS ˙ m CO2 (ton/year) Cenv ($/year) ηII CT ($/year)

Maximum second law efficiency

Multi-objective optimization

25.000 95.000 64.958 6.000 3.382 −10.001 0.703 15.086 14.833

24.918 95.000 63.839 6.002 2.000 −10.000 0.899 19.855 19.523

24.999 95.000 64.999 6.000 3.339 −10.000 0.709 15.066 14.814

22.517 22.767 13.170 15.675 0.404 0.002 1.788 8.982 3.617 14.425 2.250 4.413 5.747 0.427 7.363 0.651 0.536 8.656

23.340 23.670 17.501 19.504 0.516 0.002 2.173 9.898 7.384 31.277 2.809 5.917 17.353 0.559 8.051 0.824 0.677 10.521

22.365 22.615 13.157 15.870 0.404 0.002 1.781 8.978 3.651 14.542 2.244 4.408 5.907 0.428 7.384 0.654 0.539 8.623

779.107 0.264 9650.379

946.936 0.413 13,305.276

776.145 0.273 9658.271

can see the marked decrease (35.9%) in environmental cost due to the lower emission rates of carbon dioxide. Total heat exchange surface areas of the all heat exchangers are decreased by 6.5% and power consumption of compressor is reduced by 36.0% when R717 is applied instead of R1234yf in VCRS. COPCVCARS of the refrigeration system is increased by 13.8% in accordance with the increase in exergy efficiency. Figure 7 shows the pareto optimal solutions for the integrated cascade cycle operated with R717 in VCRS. Best final answer chosen by TOPSIS is again skewed towards left bottom of the Pareto frontier which refers to lower annual cost and second law efficiency. At this point, corresponding objective function values are 9710.213 ($/year) and 0.285. Table 12 reports the thermodynamic properties of each compared CVCARS cycle at design point obtained from TOPSIS anlaysis.

Fig. 6 Pareto optimal solutions for CVCARS working with R290 in VCRS

4.2 Sensivity analysis Multi objective design optimization problems involve decision variables having contradictory effects between them and variations of these decision parameters greatly influence the perfomance of multiple objectives. In this study, design point chosen by the TOPSIS decision making method for each cycle configuration is selected as pivot point and the effects of various decision variables on problem objectives are evaluated based on this design point. Figure 8 investigates the effects of increasing absorber temperatures on different performance indexes of the refrigeration system. As absorber temperature increases from 15 °C to 25 °C, remarkable increases are observed in heat load rates of absorber, generator and solution heat exchanger while input conditions of remaining system equipments are kept constant. Increase in themal load in each mentioned component gives rise to the amount of solution circulation throughout the absorption cycle and cause more required pump work, which inevitably entails a reduction in COPVARS and COPCVCARS rates, however COPVCRS is not affected by the variations in absorber temperature as it is expected because cascade condenser and evaporator temperatures stay constant. Exergy efficiency of the system gradually decreases as a result of the increase in exergy destruction in the generator. Total annual cost of the system is markly decreased due to the reduction in total heat exchange area of each heat exchanger in the system, but also the gradual reduction in socio-enviromental cost associated with carbon emissions. These deductions are valid for each compared cycle configuratio as can be seen in Fig. 8. Figure 9 shows the variations of different design objectives of the integrated cascaded refrigeation cycle while generator temperatures varying between 95 °C and 105 °C. Generator is an important and indispansible component of the refrigeration

Heat Mass Transfer Table 11

Optimal results for CVCARS working with R717 in VCRS Minimum total annual cost

Maximum second law efficiency

Multi-objective optimization

24.999 95.001 65.000 6.000

24.633 95.001 64.275 6.028

24.999 95.001 64.998 6.000

2.526 −10.000 0.700 εSHX ˙ Q (kW) 15.071 cond ˙ Q 14.818 cas;cond (kW) ˙ Q (kW) 22.571 abs ˙ Qgen (kW) 22.821 ˙ Q 12.942 evap (kW) ˙ Q 15.607 sol;HEX (kW) ˙ Q 0.404 reg;HEX (kW) W˙ sol;pump (kW) 0.002 W˙ comp (kW) 2.017 2 8.979 Acond (m ) 2.292 Acas, cond(m2) 14.346 Aabs(m2) 2.250 Agen(m2) 4.162 Aevap(m2) 5.665 ASHX(m2)

2.002 −10.000 0.899 19.583 19.256 23.055 23.380 16.875 19.659 0.515 0.002 2.560 9.852 3.700 30.962 2.769 5.471 17.412

2.462 −10.004 0.746 15.074 14.821 21.584 21.834 12.950 16.597 0.405 0.002 2.012 8.979 2.348 15.438 2.225 4.164 7.011

Tabs (°C) Tgen (°C) Tcond (°C) Tcas, cond (°C) Toverlap (°C) Tevap (°C)

ARHX(m2) COPVCRS COPVARS COPCVCRAS ˙ m CO2 (ton/year) Cenv ($/year) ηII CT ($/year)

0.427 6.413 0.649 0.521 9.766 878.991 0.259 9640.379

0.553 6.590 0.823 0.650 12.392 1115.329 0.397 13,141.009

0.427 6.434 0.678 0.543 9.741 876.647 0.285 9710.213

cycle in which inherent water vapour of the solution is seperated and sent to the condenser. Any increase in heat load of the generator induce a decrease in heat load rates of absorber and solution exchnager albeit conduce a considerable increase in other remeaining heat exchanger equipments. Combinatorial variations of heat loads of these devices entail a reduction in the solution circulation between absorber and generator causing a decrese in power consumption of the solution pump which increases COPCVCARS and COPVARS. Peformance coefficient of the low temperature VCRS is not influenced due to the fixed thermal conditions during temperature variation in the generator. It is seen that exergy efficiency of the refrigeration is slightly increased for each cycle configuration given in Fig. 9. Total annual cost of the system marginally increases due to the gradual increases in total heat exchange areas of heat exchange devices and resulted from

Fig. 7 Pareto optimal solutions for CVCARS working with R717 in VCRS

the increase in the operational and social cost incurred by the excessive increase in the needed compressor work. Figure 10 visualizes the variations of the different performance indexes of the refrigeration system with increasing Table 12 Thermal conditions of each refrigeration cycle base on the design point found by TOPSIS (°C)

LiBr-H2O/ R1234yf

LiBr-H2O/ R134a

LiBr-H2O/ R290

LiBr-H2O/ R717

1

−10.053

−10.000

−10.003

−10.000

2 3 4 5 6

29.076 8.777 −10.053 6.000 40.939

31.751 8.665 −10.000 6.001 40.939

20.951 9.340 −10.003 6.001 40.939

39.606 8.463 −10.004 6.000 40.939

7 8 9 10 11 12 13 14 15 16

24.993 24.993 71.979 95.002 45.567 45.512 65.000 45.000 29.400 6.005

25.000 25.000 74.764 95.000 42.501 41.781 65.000 45.000 29.400 6.001

25.000 25.000 72.214 95.000 45.313 44.992 65.000 45.000 29.400 6.000

25.000 25.000 74.534 95.001 42.771 41.998 65.000 45.000 29.400 6.000

17 18 19 20 21 22 23 24

22.001 24.683 115.000 109.589 26.116 62.000 19.946 18.648

22.000 24.570 115.000 109.820 26.173 62.000 20.000 18.621

22.000 24.675 115.000 109.615 26.195 62.000 20.000 18.565

22.000 24.581 115.001 109.802 26.176 62.000 20.000 18.587

Heat Mass Transfer

Fig. 8 Influence of absorber temperatures on design parameters as well as COP of various cyles in the integrated refrigeration system

condenser temperatures. As condenser temperatures increases 55 °C to 65 °C while input conditions of other thermal devices as well as the secondary fluid at the inlet and outlet of the condenser stays constant, numerical values of the performance coefficients of each different cycle in the refrigeration system

slightly fall. This is resulted from the increase in the amount of circulation of the solution across the absorption cycle, which is due to increase in heat load rates of solution heat exchanger and absorber and corresponding decreases for other system components. Variational changes in the imposed heat load of

Fig. 9 Influences of varying generator temperatures over various performance indexes of the cascaded refrigeration system

Heat Mass Transfer

each cycle component leads to reduction in COP rates, except that for vapor compression cycle as shown in Fig. 10. Decrease in the total annual cost of the refrigeration system with increasing condenser temperatures is the result of the reduction in heat exchange area of each heat exchange device (apart from solution heat exchnager and absorber) which leads to a marked decrease in investment cost, accompanied by the gradual decreases in operational and social cost associated with the compressor work. It is also observed that second law efficiency of the system is inversely affected by the condenser temperature increases as this increase induce higher exergy destruction rates because of the increasing temperature difference between the refrigerant flowing though condenser and external cooling water used as a secondary fluid. Figure 11 shows the influence of the increasing cascade condenser temperatures on performance coefficients of each cycle in the refrigeration system along with design objectives including total annual cost and second law efficiency for each cycle configuration operating with different refrigerants in VCRS. Cascade condenser temperature refers to the condensing temperature in the cascade condenser and is a decisive system parameter playing an important role on the performance of each cycle in the refrigration system. As cascade condenser temperatures increase 6.0 °C to 16.0 °C, power consumption of the compressor in VCRS expectedly increases. This increase cause a considerable decrease in COPVCRS rates. However, increase in condensation temperatures improves performance coefficient of absorption cyle (COPVARS) and integrated cascaded refrigeration cycle (COPCVCARS). Second law efficiency

of the refrigeration cycle is positively affected by this temperature increase, except for the cycle using R1234yf in VCRS. Increases in total heat exchnager area and the required compressor work with increasing cascade condenser temperature cause a mammoth increase in total annual cost of the cycle. Figure 12 depicts the effects of increasing evaporator temperatures over different performance coefficients and design objectives of the refrigeration system. Increase in evaporator temperature between −20 °C and − 10 C leads to a decline in electric power consumption of VCRS compressor due to the increase in the density of the refrigeration in the evaporator outlet, which consequently causes reduction in operational and environmental cost related with compressor work. Overall COP of the refrigeration system is also increased with the raise of evaporation temperatures. Exergy efficiency shows a decreasing trend and then gradually incraeses with the increment of evaporator temperatures. This behavior can be explained by the changing trend of the temperaure difference between the refrigerant and secondary fluid in the evaporator. Rise in investment cost due to the increases in total heat exchange surface area of the system is compansated for the above mentioned reducton in operational and envioronmental cost and this results in a relatively result increase in total annual cost compared to former analysis. Figure 13 shows the variations of the performance coefficients of different cycles in the refrigeration system and design objectives with increasing values of solution heat exchahger efficiencies for each cycle configuration operating with different refrigerants in VCRS. Efficiency of the solution heat

Fig. 10 Variations of the different performance indexes of the system with increasing condenser temperatures

Heat Mass Transfer

Fig. 11 Influences of varying cascade condenser temperatures on performance coefficients and design objectives

exchanger not only directly affects asborber inlet temperatures but also substiantially influence the overall performance coefficient and second law efficiency of the cascaded refrigeration system. It is also understood from the multi objective optimization analysis results that variation of this design parameter between its allowable search space is the main factor creating trade-off between design objectives. As this efficiency value

varies between 0.6 to 0.9 while design parameters of remaining system components staying fixed, the heat load of solution heat exchanger slightly increases while decremental decreases are seen in the heat load of absorber and generator. These variational changes cause an increase in performance coefficient of absorption cycle as well as integrated refrigeration cycle. Improvement in COP rates leads to a marginal increase in

Fig. 12 Effect of varying evaporator temperature on different performance indexes of the refrigeration system

Heat Mass Transfer

Fig. 13 Variations of different performance indexes of the refrigeration system with increasing solution heat exchanger efficiency

overall exergy efficiency of the refrigeration system. Operational and envioronemtal costs are not clearly affected by the varation of efficiency of the solution heat exchanger since the power consumption of the comperssor in VCRS has nothing to the with this variation Due to relatively smaller increases in the solution heat exchanger surface area which is the only factor influencing the investment cost for this case, total

annual cost of the system shows a slight increase for each cycle configuration operated with different refrigeratnts in VCRS. Figure 14 shows the effects of varying overlap temperatures on perfomance coefficients of different cycles in the refrigerant system and two mentioned design objetives. Overlap temperature refers to the temperature difference between two streams in the cascade condenser. As this temperature difference varies

Fig. 14 Effects of varying overlap tempeatures on different perfomance indexes of the combined refrigeration system

Heat Mass Transfer

between 2.0 to 10.0 while input design conditions of remaining system conponents are fixed, amount of heat load in absorber, generator and condenser increases. This increase leads to a decrement in performance coefficient of absorption cycle as well as exergy efficiency. Resulted from the small increases in total heat exchange surface area of each heat exchnage device in absorption cycle, total annual cost of the refigeration system incerases with increasing overlap temperatures for each cycle configuration compared in Fig. 14.

5 Conclusion This study comparatively investigates the applicability of an integrated cascaded absoption compression refrigeration system operated with different refrigerants such as R134a, R1234yf, R717 and R290 in the vapor compression cycle. Single and multiobjective optimization of CVCARS operating with above mentioned different working fluids are accomplished by using metaheuristic optimization algorithm called Artificial Cooperative Search (ACS) to obtain optimum design points of the refrigeration system for each cycle configuration. Seven design variables which includes operational parameters such as overlap temperature, solution heat exchanger efficiency, absorber, generator, condenser, evaporator, and cascade condenser temperatures are considered. Two different design objecives are considered for simultaneous and individual optimization of the refrigeration system. One is total annual cost comprising opeational, investement and social cost due to carbon emission and the other is second law efficiency of the system. These contradictory but complementary design objectievs are concurrently and seperately optimized and optimal results are compared. Single objective optimization results show that minimum total annual cost is obtained by the CVCARS with working R717 in VCRS while refrigeration system operating with R290 in VCRS has the maximum second law efficiency. Then multi objective optimization is applied to obtain a set of nondominated solutions called Pareto solutions which are in essence trade-off between design objectives. These solutions are nondimensionalized and best answer among them is found by the famous decision maker TOPSIS. Best answer chosen by TOPSIS is inclined to minimum total annual cost and second law effieciency for each cycle configuration. Sensitivity analysis is performed and influences of design variables on differemt performance indexes of the refrigeration system are comparetively discussed. It is also seen that multi objective optimization performance of Artificial Coopreative Search algorithm is very promising and satisfactory, deduced by the successful distribution of the non-dominated solutions across the Pareto curve. Optimal values obtained by means of single and multi objective optimization along with the outcomes of sensitivty analysis can be reliably used as a benchmark for the future studies

dealing with thermal modelling and design of a compression absorption refrigeration system.

Compliance with ethical Standarts Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest. Ethical approval This article does not contain any studies with human participants or animals performed by any of the authors. Informed consent Informed consent was obtained from all individual participants included in the study. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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7.

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13.

Bakhtiari B, Fradette L, Legros R, Paris J (2011) A model for analysis and design H2O-LiBr absorption heat pumps. Energ Convers Manage 52:1439–1448 Florides GA, Kalogirou SA, Tassou SA, Wrobel LC (2003) Design and construction of LiBr-water absorption machine. Energ Convers Manage 44:2483–2508 Gebreslassie BH, Gosalbez GG, Jimenez L, Boer D (2009) Design of environmentally conscious absorption cooling systems via multiobjective optimization and life cycle assessment. Appl Energy 86: 1712–1722 Godarzi AA, Jalilian M, Samimi J, Jokar A, Vesaghi MA (2013) Design of a PCM storage system for a solar absorption chiller based on exergoeconomic analysis and genetic algorithm. Int J Refrig 36: 88–101 Sachdeva G, Jain V, Kachhwaha SS (2013) Exergy analysis of a vapor compression-vapor absorption cascade system. IJACR 21:1–10 Jain V, Sachdeva G, Kachhwaha SS, Patel B (2016) Thermoeconomic and environmental analyses based multi-objective optimization of vapor compression-absorption cascaded refrigeration system using NSGA-II technique. Energ Convers Manage 113:232–242 Chen Y, Han W, Sun L, Jin H (2015) A new absorptioncompression refrigeration system using a mid-temperature heat source for freezing application. Energy Procedia 75:560–565 Goktun S, Er ID (2001) Optimum performance of a solar assisted combined absorption-vapor compression system for air conditioning and space heating. Sol Energy 71:213–216 Kairouani L, Nehdi E (2006) Cooling performance and energy saving of a compression-absorption refrigeration system assisted by geothermal energy. Appl Therm Eng 26:288–294 Sun ZG (2008) Experimental investigation of integrated refrigeration system (IRS) with gas engine, compression chiller and absorption chiller. Energy 33:431–436 Fernandez-Seara J, Sieres J, Vazquez M (2006) Compressionabsorption cascade refrigeration system. Appl Therm Eng 26: 502–512 Jain V, Kachhwaha SS, Sachdeva G (2014) Exergy analysis of a vapour compression-absorption cascaded refrigeration system using modified Gouy-Stodola equation. Int J Exergy 15:1–23 Jain V, Sachdeva G, Kachhwaha SS (2015) Thermodynamic modelling and parametric study of a low temperature vapourcompression absorption system based on modified Gouy-Stodola equation. Energy 79:407–418

Heat Mass Transfer 14.

Jain V, Sachdeva G, Kachhwaha S (2015) Energy, exergy, economic and environmental (4E) analyses based comparative performance study and optimization of vapor compression-absorption integrated refrigeration system. Energy 76:816–832 15. Cimsit C, Ozturk I, Kıncay O (2015) Thermoeconomic optimization of LiBr-H2O/R134a compression-absorption cascade refrigeration cycle. Appl Therm Eng 15:105–115 16. Jain V, Sachdeva G, Kachhwaha S (2015) NLP model based thermoeconomic optimization of vapor compression-absorption cascaded refrigeration system. Energ Convers Manage 93:49–62 17. Sayyadi H, Nejatolahi M (2011) Multiobjective optimization of a cooling tower assisted vapor compression refrigeration system. Int J Refrig 34:243–256 18. Yang F, Cho H, Zhang H, Zhang J (2017) Thermoeconomic multiobjective optimization of a dual loop organic Rankine cycle (ORC) for CNG engine waste heat recovery. Appl Energy 205:1100–1118 19. Keshtkar MM, Talebizadeh P (2017) Multi-objective optimization of cooling water package based on 3E analysis: a case study. Energy 134:840–849 20. Duan C, Wang X, Shu S, Jing C, Chang H (2014) Thermodynamic design of Stirling engine using multi-objective particle swarm optimization algorithm. Energ Convers Manage 84:88–96 21. Shamoushaki M, Ehyaei MA, Ghanatir F (2017) Exergy, economic and environmental analysis and multi objective optimization of a SOFC-GT power plant. Energy 134:515–531 22. Patel V, Savsani V, Mudgal A (2017) Many-objective thermodynamic optimization of Stirling heat engine. Energy 125:629–642 23. Aminyavari M, Mamghani AH, Sirazi A, Najafi B, Rinaldi F (2016) Exergetic, economic, and environmental evaluations and multiobjective optimization of an internal-reforming SOFC-gas turbine cycle coupled with a Rankine cycle. Appl Therm Eng 108:833–846 24. Damavandi MD, Forouzanmehr M, Safikhani H (2017) Modeling and Pareto based multi objective optimization of wavy fin-andelliptical tube heat exchangers using CFD and NSGA-II algorithm. Appl Therm Eng 111:325–339 25. Raja BD, Jhala RL, Patel V (2017) Many-objective optimization of cross-flow plate-fin heat exchanger. Int J Therm Sci 118:320–339 26. Liu C, Bu W, Xu D (2017) Multi objective shape optimization of a plate-fin heat exchanger using CFD and multi-objective genetic algorithm. Int J Heat Mass Transf 111:65–82 27. Mirzaei M, Hajabdollahi H, Fadakar H (2017) Multi objective optimization of shell-and-tube exchanger by constructural theory. Appl Therm Eng 125:9–19 28. Sanaye S, Hajabdollahi H (2010) Multi objective optimization of shell and tube heat exchangers. Appl Therm Eng 30:1937–1945 29. Civicioglu P (2013) Artificial cooperative search algorithm for numerical optimization problems. Inform Sciences 229:58–76 30. Colorado D, Rivera W (2015) Performance comparison between a conventional vapor compression and compression-absorption, single-stage and double-stage systems used for refrigeration. Appl Therm Eng 87:273–285 31. Jain V, Sachdeva G, Kachhwaha S (2014) Performance analysis of a vapour compression-absorption cascaded refrigeration system with under sized evaporator and condenser. J Energy South Afr 25:23–36 32. Colorado D, Velazquez V (2013) Exergy analysis of a compressionabsorption cascade system for refrigeration. Int J Energy Res 37: 1851–1865 33. Wang L, Ma A, Tan Y, Cui X, Cui H (2012) Study on solar-assisted cascade refrigeration system. Energy Procedia 16:1503–1509 34. Garimella S, Brown A, Nagavarapu A (2011) Waste heat driven absorption/vapor-compression cascade refrigeration system for megawatt scale, high-flux, low-temperature cooling. Int J Refrig 34:1776–1785 35. Chinnappa J, Crees M, Srinivasa Murthy S, Srinivasan K (1993) Solar-assisted vapor compression/absorption cascaded airconditioning systems. Sol Energy 50:453–458

36.

Marimon M, Arias J, Lundqvist P, Bruno J, Coronas A (2011) Integration of trigeneration in an indirect cascade refrigeration system in supermarkets. Energy Build 43:1427–1434 37. Jain V, Kachhwaha SS, Sacdeva G (2013) Thermodynamic performance analysis of a vapor compression-absorption cascaded refrigeration system. Energy Convers Manag 75:685–700 38. Kotas TJ (1995) The exergy method of thermal plant analysis. Krieger Publishing Company, Florida 39. Arora CP (2000) Refrigeration and airconditioning. Tata Mcgraw Hill Publishing Company Limited, New Delhi 40. Maya CR, Ibarra JJP, Flores MB, Gobzalez SRG, Covarrubias CM (2012) NLP model of a LiBr-H2O absorption refrigeration system for the minimization of the annual operating cost. Appl Therm Eng 37:10–18 41. Misra RD, Sahoo PK, Gupta A (2005) Thermoeconomic optimization of LiBr/H2O absorption chiller using structural method. J Energy Resour-Asme 127:119–124 42. Mehr AS, Zare V, Mahmoudi SMS (2013) Standard GAX versus hybrid GAX absorption refrigeration cycle : from the view point of thermoeconomics. Energy Convers Manag 76:68–82 43. Cimsit C, Ozturk IT (2012) Analysis of compression-absorption cascade refrigeration cycles. Appl Therm Eng 40:311–317 44. Gomri R (2013) Simulation study on the performance of solar/ natural gas absorption cooling chillers. Energy Convers Manag 65:675–681 45. Khan J, Zubair S (1999) Design and performance evaluation of reciprocating refrigeration systems. Int J Refrig 22:235–243 46. Aminyavari M, Najafi B, Shirazi A, Rinaldi F (2014) Exergetic, economic and environmental (3E) analyses, and multi-objective optimization of a CO2/NH3 cascade refrigeration system. Appl Therm Eng 65:42–50 47. Rezayan O, Behbahaninia A (2011) Thermoeconomic optimization and exergy analysis of CO2/NH3 cascade refrigeration systems. Energy 36:888–895 48. Bell IH, Wronski J, Quoilin S, Lemort V (2014) Pure and pseudopure fluid Thermophysical property evaluation and the open-source Thermophysical property library CoolProp. Ind Eng Chem Res 53: 2498–2508 49. Sanaye S, Shirazi A (2013) Four E analysis and multi objective optimization of an ice thermal storage for air-conditioning applications. Int J Refrig 36:828–841 50. Wang J, Zhai Z, Jing Y, Zhang C (2010) Particle swarm optimization for redundant building cooling heating and power system. Appl Energy 87:3668–3679 51. Gnielinski V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng 16:359–367 52. Incorpera FP, DeWitt DP (2002) Fundamental of mass transfer, 5th edn. John Wiley & Sons, New York 53. Chato JC (1962) Laminar condensation inside horizontal and inclined tubes. ASHRAE J 4:52–60 54. Song B (1989) Design and calculation of falling film evaporator for horizontal tube of thermodynamic steam. Technology of Water Treatment 15:39–44 55. Hofmann L, Greiter I, Wagner A, Weiss V, Alefeld G (1996) Experimental investigation of heat transfer in horizontal tube falling film absorber with aqueous solutions of LiBr with and without surfactants. Int J Refrig 19:331–341 56. Turgut MS, Demir GK (2017) Quadratic approximation-based hybrid artificial cooperative search algorithm for economic emission load dispatch problems. Int Trans Electr Energ Syst 27:1–14 57. Kumar R, Kaushik SC, Kumar R, Hans R (2016) Multi-objective thermodynamic optimization of an irreversible regenerative Brayton cycle using evolutionary algorithm and decision making. Ain Shams Eng J 7:741–753