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Thermoeconomic Optimization and Exergy Analysis of Transcritical CO2 Refrigeration Cycle with an Ejector

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Thermoeconomic Optimization and Exergy Analysis of Transcritical CO2 Refrigeration Cycle with an Ejector energyequipsys/ Vol 4/No1/June 2016/ 43-52 Energy Equipment and Systems http://energyequipsys.ut.ac.ir www.energyeuquipsys.com Thermoeconomic optimization and exergy 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 transcritical cycle 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 entropy production 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 energy 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
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