energyequipsys/ Vol 4/No1/June 2016/ 43-52

Energy Equipment and Systems

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Thermoeconomic optimization and analysis of transcritical CO2 refrigeration cycle with an ejector

Authors ABSTRACT a* Ali Behbahani-nia The purpose of this research is to investigate thermoeconomic a Saeed Shams optimization and exergy analysis of transcritical CO2 refrigeration cycle with an ejector. After modeling thermodynamic equations of a Mechanical Engineering elements and considering optimization parameters of emerging Department, K.N. Toosi University of temperature of gas of cooler (Tgc) , emerging pressure of cooler's Technology Tehran, Tehran, Iran gas (Pgc) , and evaporative temperature (Tevp) , optimization of target function is done. Target function indicates total expenses of the system during a year which is consisted of expenses of entering exergy and spending on the system's equipment. Optimized amplitude of decision variables are gained by the balance between the entering exergy and yearly initial capital investing. Results indicate reduction Article history: in yearly total expenses of system (34%) and enhancement in Received : 29 December 2015 thermodynamic functionality coefficient and exergetic efficiency in Accepted : 9 February 2016 optimum point toward end point.

Keywords: Exergy, Refrigeration, Thermoeconomic, Transcritical CO2. 1. Introduction By the introduction of transcritical time or in other words warming feature of refrigeration cycle with an ejector by [1] in this refrigerant is 1300 times more than CO2 1990, an improving study initiated on this [3]. Features which have brought about wide cycle. Noticeable increase in COP, reduction application of CO2 in refrigeration and air of exergetic destructions during throttling conditioner systems are of it being non-toxic, procedure, application of CO2 as a refrigerant, inexpensive, non-flammable, in-explosive, and also facilitating in pressure control of gas non-corrosive, available, harmless for cooler are unique features of proposed environment, not being of CFCs and HCFCs, transcritical CO2 refrigeration cycle with an its low critical temperature, and high pressure ejector [2]. functionality [4, 5]. Last two features refer to Global warming and intense climate the advantage of application of CO2 in changes has brought about global concern and compared to subcritical development of refrigeration systems with cycles. refrigerants with permissible limit of GWP; Analysis of thermodynamic transcritical for instance, refrigerant R134a has GWP CO2 refrigeration cycle with an ejector was amplitude of 1300 with 100 of years period of first performed by [6] and [7]. It is indicated that "ejector" has more effect on enhancement of COP in transcritical rather *Corresponding author: Ali Behbahani-nia than subcritical [8]. Despite this, there are Address: Mechanical Engineering Department, K.N. Toosi University of Technology Tehran, Tehran, Iran inevitable exergy destructions in the system E-mail address: [email protected] because of irreversibility of mixing procedure 44 Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016

of ejector which decreases functionality of the ( ) enthalpy system [9]. Finally, studies which have been done in the field of ejector compressive pressure refrigeration and by utilizing various temperature refrigerants have been reviewed by [10] and fouling coefficient their thermodynamic and exergetic functionalities have been compared. ( ) mass flow based on In all the studies above, target function was meter unit to increase thermodynamic functionality or compressor decrease or exergetic gas cooler destruction, which in some cases application of more expensive equipment was necessary. expansion value Consequently, there was desperate need for an evaporator economical approach toward transcritical CO2 Separator refrigeration cycle with an ejector. The purpose of this research is thermoeconomical Fuel analysis of the mentioned cycle to find a way P Product to optimize the relation between initial capital investment and the expense of the gained Destruction and also to minimize Lost thermoeconomical target function. temperature of warm In this research, thermodynamic equations source

governing the equipment have been modeled temperature of cold and then exergetic and thermodynamic source analysis have been run on them. Finally, we Out Output have equations of cost of buying equipment and thermoeconomic equation is produced by ( ) negative width making the costs annually and summing them ( ) density by cost of electricity consumed by compressor ( ) viscosity yearly. Thermoeconomic function is optimized by considering decision variables suction ratio of Tgc , Pgc , Tevp . ̇ ( ) heat ratio

diffuser Symbols mixing chamber ̇( ) capital investment initial flow (current) expense secondary total heat transmission flow(current) coefficient input thermodynamic functionality Isotropic efficiency exergetic efficiency total total

thermodynamic efficiency 2.Thermodynamic analysis

exergy's destruction Transcritical CO2 refrigeration cycle with an annualizing ejector is consisted of gas cooler, separator, coefficient ejector, compressor, evaporator, and a throttle valve which is indicated in Fig.1 with its ejector's index diagram. The mentioned cycle sucks the ̇ ( expense ratio refrigerant from evaporator using the ejector and increases the pressure in order to reduce expense by exergy's load of the compressor. After that, vapor phase unit is separated from liquid phase by the ̇ ( ) exergy's ratio separator, vapor phase goes to gas cooler by

Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016 45 passing through the compressor and becomes Schematic picture of ejector and pressure cool and finally output of gas cooler plays the change in its length are indicated in Figs. 2 role of mover vapor of the ejector so that it can and 3. The first part of ejector is its nozzle for be able of sucking and liquid phase goes to which evaporator for refrigeration. Thermodynamic equations governing equipment of the system (1) are shown in Table 1. Ejector's model based of operation performed by assumption of constant- and pressureof mixing chamber is simulated by (2) [11] and any shock effect is stipulated in . output of nozzle and diffuser and also interflow of ejector is assumed one- In the suction part (second part of ejector), dimensional and equilibrated. and are obtained using

Fig. 1. Transcritical CO2 refrigeration cycle with an ejector and its P-H diagram

Table 1. Equations of fuel's exergy and product's exergy of the cycle Product's exergy Fuel's exergy Equipment

̇ ̇ 0 Gas cooler ̇ ̇ ̇ ̇ Evaporator ̇ ̇ ̇ Ejector ̇ ̇ ̇ Separator ̇ ̇ ̇ Compressor ̇ ̇ Expansion value

̇ ̇ whole system

Fig. 2. Ejector's scheme and its functionality points 46 Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016

ignored in the gas cooler, evaporator, and

(3) connecting tubes. Thus the first law gives

̇ ̇ (12) and and . (4)

̇ ̇ . (13) Equations concerned with the mixing part Functionality coefficient of the refrigeration consist of the conservation of mass, energy cycle with an ejector is defined as and momentum for which of are unknown. Thus ̇ (14) . ̇ ̇ ̇ ̇ , (5)

3.Exergy analysis

Exergy analysis is consisted of calculation of

exergy's destruction, exergetic output, and the

proportion of exergy's loss in each element (6) and also in the whole system. Exergy's loss refers to the amount of exergy which is and released to the environment or is destructed because of irreversibility of the system.

Exergy's balance for a stable condition is

. (7) given as

In the last step there are diffuser's equations ∑ ̇ ∑ ̇ ̇ from which is calculated as ejector's outlet

enthalpy. That is ∑ ( ) ̇ (15) (8) ̇ .

Emerging refrigerant of the ejector is Exergy’s destruction is calculated in every divided into saturated vapor and saturated element of exergy's balance. That is liquid by the separator and their flow proportion must be equal to µ so that Mana ̇ ̇ ̇ ̇ . (16) functionality is stable, and it means that General equation of exergy's destruction is output quality of the ejector must be equal to given as , which causes reform of initial ̇ ̇ . (17) assumption of proportion amplitude of compression. Inside the separator, the flow is assumed to be adiabatic and stable. Exergy efficiency indicates proportion of Thus the first law gives exergy of products to fuel in each element and also in the whole system. Thus ̇ ̇ ̇ . (9) ̇ ̇ ̇ (18) Isentropic efficiency and the consuming ε ̇ ̇ . power of the compressor are given Exergy damage proportion compares (10) amplitude of exergy's damage in each element η with exergy of the whole system's fuel. Thus ̇ ̇ ̇ (11) . (19) ̇ Gas cooler operates in variable temperature, constant pressure higher than critical points, In order to analyze the system using second and evaporator operates in saturated rule of thermodynamic you need to define temperature and pressure. Pressure fall is fuel's exergy and product's exergy of each element. Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016 47

Product is representative of desirable part mass or energy or exergy to the system or and fuel is the source by use of which, our emerging from the system, exergy's product is produced. Table 1 indicates the destruction occurs due to irreversibility inside fuel's exergy and product's exergy of each the system. The expense ratios for this element. particular system are given as Exergy damage for each element separately ̇ ̇ (29) is given respectively as , ̇ , (20) ̇ ̇ , (30)

(21) ̇ , ̇ ̇ (31)

and (22) ̇ , ̇ ̇ (32) , and the equilibrium equation for the expenses ̇ (23) on elements of the system is defined as and (33) ∑ ̇ ̇ ∑ ̇ ̇ ̇ ̇ ̇ ̇ . (24) In thermoeconomical analysis of a heat Moreover, for the entire system the following system, definite quantities, which are known equations for thermoeconomical variables, play an important role. These quantities include mean ̇ ̇ , (25) expense of unit of fuel , mean expense of unit of product ( , rate of exergy's ̇ ̇ , (26) destruction ( ̇ ), rate of exergy's wasting (27) expense ( ̇ ) and exergo-economic factor ̇ ̇ ( ). In balanced equation of expense for an and element, there is no expense which would be directly related to the exergy's destruction. Hence expenses related to destructions of an . (28) element are hidden expenses which can be shown in thermoeconomical analysis. hold. Eventually, the analysis would propose destruction expenses are defined as ways of reaching to the most efficiency of ̇ ̇ (34) exergy to designer, but there is also a . tendency to minimize expenses, so we use By considering equations above and thermoeconomic analysis to reach our target. assuming ̇ to be constant, balanced equation of costs is indicated as 4. Thermoeconomic analysis ̇ ̇ ̇ ̇ (35) Exergy is a basis of capital investing in heat system. Thermoeconomic is based on the fact and ̇ that exergy is the only logical source to (36) ̇ . allocate expenses related to the financial ̇ exchanges of the heat system and Those elements which are greater in environment and its inefficiency sources. It amplitude of " ̇ " must be considered more means that by each exergy's flow in the seriously. Shortage in the amplitude of " " in system, expenses are allocated with the an element indicates that, perhaps, one could currency of exergy and, consequently, total reach the thriftiness limit by reforming the exergy's flow is converted to financial flow. efficiency of that element. In fact, exergy, which is a dynamical concept, The price of a compressor is given by [12]: is converted to currency which is a financial concept. For a system which works in stable ̇ condition with so many inputs and outputs of ̇ ( ) ( ) ( ) (37) currents of mass, work, heat or interaction with the environment because of transferring

48 Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016

The price of a condenser and evaporator are (46) also given as [13]: ̇ ̇ ̇ ̇

̇ (38) Expense's balance equation and auxiliary and equation of fuel for compressor are, respectively given as ̇ (39) .

̇ ̇ ̇ ̇ (47) The price of ejector is given by El-Sayed as

(40) and ̇ ̇ .

̇ ̇ ̇ ̇ . (48) It should be noticed that these prices must be updated to the year 2014. Thus, For throttle valve the following

̇ ̇ , (41) (49) ̇ ̇ ̇

where and are expense holds. Expense's balance equation and coefficients of Swift & Marshal in the auxiliary equation of fuel for evaporator are, reference and current year which are brought respectively, given as by Peter & Timmerhaus, 1991 [333].

Total capital investment is converted to ̇ ̇ ̇ expense rate by using two factors of "CRF"

and "H" using ̇ (50)

(42) and ̇ ̇ Auxiliary equations define the base of fuel ̇ ̇ . (51) rule for gas cooler, compressor, and evaporator. According to this rule, total Finally, there exist 6 expense's balance expenses concerned with reduction of exergy equations and 3 auxiliary equations of fuel of a flow are equal to mean expense of exergy which are equal to the number of the which is added for the previous elements. unknown quantities, and now one can solve Based on this rule, numbers of the equations the system of equations for the9 unknown are obtained from the number of the flows quantities. which are known as fuel. Considered parameters of system's design The equation of expense's balance the are indicated in Table 2. corresponding auxiliary equation of fuel for the gas cooler which is written with regards to the duty of gas cooler (which is cooling flow Table 2. Assumed parameters of the cycle number 5) are given as 300 KPa

̇ ̇ 0.9

0.8 ̇ ̇ (43)

0.75 and ̇ 65 kw ̇ ̇ . (44) ̇ ̇ 298 For the ejector these equations become 298 283 ̇ ̇ ̇ ̇ . (45) N 10 years The expense's balance for the H 3000 hours separatorwhich is the next equipment is given I 8% as 0.07 $/kW.h

Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016 49

5. Optimization 6. Discussion and Conclusions

Thermoeconomical target function is Basic design of the cycle is designed using indicated in the term 53 and consists of yearly assumed parameters of Table 2 and change capital investment of the equipment and effects of decision's variables on exergy's yearly electricity consumed by the destruction and its capital investment are compressor, and its decision variables are considered. emerging temperature of the gas cooler , Figure 3 indicates exergy's destruction changes based on gas cooler's 7.c of evaporator. emerging pressure of gas cooler , and Total exergy's destruction is increased by evaporator's temperature which their increase of gas cooler's pressure and relation is indicated as temperature. The most exergy's destruction is caused by gas cooler which has a proportion of (52) 45% of the total exergy's destruction. . Figure 4 indicates exergy's destruction Finally one has changes based on evaporator's temperature in the temperature of 20˚C and pressure of 9000 kpa of gas cooler. By increase of evaporator's temperature, total exergy's destruction ∑ ̇ ∑ ̇ (53) decreases. Also, exergy's destruction of each ̇ element decreases except in "expansion value".

̇ ̇ ̇ ̇ ̇ ̇ ̇ ⁄ (54) ̇

28 P=8000 P=8500 23 P=9000 P=9500 P=10000 18 P=10500 P=11000 13

8 Total Exergy TotalExergy Distruction(KW) 3 20 25 30 35 40 45 outlet temperature of gas cooler (°C) Fig. 3. Exergy's destruction changes based on gas cooler's temperature

14

13 12 11 10 9 8 7 6 5 -10 TotalExergy Distruction(KW) -5 0 5 10 Evaporator temperature (°C) Fig. 4. Exergy’s destruction changes based on evaporator's temperature 50 Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016

Figure 5 indicates that by increasing gas pressure of gas cooler and for the compressor cooler's pressure, exergy's destruction it decreases at first and then it increases. increases. Figure 7 indicates total capital investment's Figure 6 indicates total capital investment's changes based on emerging temperature of changes based on emerging pressure of gas gas cooler at the pressure of 9000kpa and cooler which is plotted for the emerging gas evaporator's temperature of 7˚C. By increase cooler in temperature range of 20 to 40. This of the temperature, compressor's operation is diagram indicates thermoeconomical optimum increased and following that, capital point in various temperatures, in which investment of the compressor, ejector, and gas optimum pressure point is located out of cooler increase. Ejector's pressure ratio determined interval for temperatures below increases from 1.24 to 1.44 and suction ratio decreases from 0.93 to 0.22. This diagram is 35˚C. Minimum amplitude of target function plotted in different pressures of the gas cooler is the first point of the interval and optimum and by decrease of the pressure the sharp point is visible for the temperatures higher slope of the end of the diagram becomes than 35˚C. sharper and moves forward, and these changes Capital investment for gas cooler and is visible up to critical temperature and ejector are reduced by increasing emerging pressure of CO2 in 30.98˚C and 7377 kpa.

10

9.5 9 8.5 8 7.5 7

6.5 Total Exergy TotalExergy Distruction(KW) 6 9000 9500 10000 10500 11000 Outlet Pressure of gas cooler (KPa) Fig. 5. Exergy’s destruction changes based on gas cooler's pressure

1.1 Tgc=42C 1 Tgc=40C Tgc=38C

0.9 Tgc=34C Tgc=30C 0.8 Tgc=25C Tgc=20C

0.7 c_ele c_ele ($/kw.h) 0.6

0.5

0.4 9000 10000 11000 12000 Outlet Pressure of gas cooler (KPa) Fig. 6. Capital investment's changes based on gas cooler's pressure Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016 51

1.2 1.1 1

0.9 0.8

0.7

($/kW.h)

p

c 0.6 0.5 0.4 20 25 30 35 40 45 Outlet Temperature of gas cooler (°C) Fig. 7. Capital investment changes based on gas cooler’s temperature.

Figure 8 indicates total capital investment 7. Conclusion changes based on evaporator's temperature at the pressure of 9000kpa and gas cooler's In this article, thermoeconomical optimization temperature of 20˚C. 7˚C is the optimum method of transcritical CO2 refrigeration cycle with an ejector was presented. In the study, temperature of it. By increasing evaporator's both thermodynamic and economical aspects temperature, compressor's operation and of the cycle were considered and capital investment of the compressor and thermoeconomic optimum point of the system ejector decrease and increases in gas cooler was obtained by the target function of current and evaporator. and yearly capital investment and genetic Table 3 compares thermoeconomical optimization algorithm. optimum point and the base point (11) and Refrigeration capacity, temperature of indicates that thermoeconomical analysis warm and cool environment, evaporator's decreased product's expense up to 35%. Fuel temperature, gas cooler's temperature and expenses are also decreased about 48% which pressure are decision variables. The optimum indicates decrease of mass flow of the fuel. amplitude of decision variables are as 60% decrease in exergy's destruction and 21% , and . decrease in total capital investment are also As mentioned before, both thermodynamic functionality and exergetic efficiency of the indicated. 93% increase for both exergy's cycle have 93% increase and total yearly efficiency and thermodynamic functionality capital investment has 34% decrease in are indicated. consequence of application of this method.

0.53

0.51

0.49

0.47 ($/kW.h)

p p 0.45 c

0.43

0.41 -15 -10 -5 0 5 10 Outlet Temperature of evaporator (°C) Fig. 8. Capital investment changes based on evaporator’s temperature.

52 Ali Behbahani-nia & Saeed Shams /energyequipsys / Vol 4/No1/June 2016

Table 3. Fuel comparison in two optimum and base conditions Base point Optimum pint

̇ ,($/h) 0.2743 0.1999

̇ ,($/h) 0.2555 0.1193 ̇ ,($/h) 0.0086 0.0052

̇ ,($/h) 0.2060 0.2623

̇ ,($/h) 0.1986 0.1986 ̇ ,($/h) 0 0 ̇ ,($/h) 0.9430 0.7853

̇ ,($/h) 1.2656 0.6559 ̇ ,($/h) 2.2092 1.4413 ̇ ,($/h) 1.0248 0.4107 Exergetic efficiency of 0.1905 0.3677 the sys. % COP 3.595 6.937

,KPa 10000 9000 ,°C 40 20

,°C 5 7

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