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Thermodynamic analysis of different two-stage transcritical carbon dioxide cycles
international journal of refrigeration 32 (2009) 1058–1067
available at www.sciencedirect.com
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Thermodynamic analysis of different two-stage transcritical carbon dioxide cycles Luca Cecchinato*, Manuel Chiarello, Marco Corradi, Ezio Fornasieri, Silvia Minetto, Paolo Stringari, Claudio Zilio Dipartimento di Fisica Tecnica, Universita` di Padova, via Venezia 1, I-35131 Padova, Italy
article info
abstract
Article history:
The aim of this paper is the thermodynamic evaluation and optimisation of different two-
Received 5 February 2008
stage transcritical carbon dioxide cycles. Five different cycles are studied: basic single-
Received in revised form
stage cycle, single-throttling with two-stage compression cycle, split cycle, phase
19 August 2008
separation cycle and single-stage cycle coupled with a gas cooling circuit. Each basic cycle
Accepted 5 October 2008
is analysed for the effect of internal heat transfer between different streams of refrigerants.
Published online 1 November 2008
In the case of two-stage compression, intermediate cooling between the compressor stages is present. An analysis on the Plank cycle for intermediate pressure higher than critical one
Keywords:
is performed. Each cycle is optimised with regards to energy performance, calculating the
Refrigeration system
optimal values of both the upper and the intermediate pressures. In the case of split cycle,
Carbon dioxide
the ratio of the mass flow rate in the main stream to the one in the auxiliary stream is also
Transcritical cycle
optimised.
Comparison
ª 2008 Elsevier Ltd and IIR. All rights reserved.
Thermodynamic cycle Single-stage system Two-stage system Calculation Performance Optimization
Analyse thermodynamique de plusieurs cycles au dioxyde de carbone transcritiques bie´tage´s Mots cle´s : Syste´me frigorifique ; Dioxyde de carbone ; Cycle transcritique ; Cycle thermodynamique ; Syste´me monoe´tage´ ; Syste´me bie´tage´ ; Calcul ; Performance ; Comparison ; Optimisation
* Corresponding author. Tel.: þ39 049 827 6876; fax: þ39 049 827 6896. E-mail address: [email protected] (L. Cecchinato). 0140-7007/$ – see front matter ª 2008 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2008.10.001
international journal of refrigeration 32 (2009) 1058–1067
Nomenclature COP h L _ m n p Q s T x
1.
Q/L, coefficient of performance [-] enthalpy [J kg1] specific mechanical energy [J kg1] mass flow rate [kg s1] overall compression efficiency [-] pressure [Pa] specific refrigeration capacity [J kg1] entropy [J K1 kg1] temperature [ C] mass flow ratio [-]
Introduction
Carbon dioxide is one of the oldest refrigerants, as it was already employed at the end of the nineteenth century, mainly where safety was essential. However, when, around 1931, synthetic refrigerants came into use, CO2 began its decline, because the new fluids provided best energy efficiency with cheaper and more reliable equipment. High critical pressure (7.38 MPa) and rather low critical temperature (31.06 C) summarise the main drawbacks of carbon dioxide. Nevertheless today CO2 is gaining more and more favour thanks to its very low environmental impact. In 1994 the Norwegian professor Gustav Lorentzen first proposed again this refrigerant as a working fluid for vapour compression inverse cycles and from that moment many other Authors have extensively studied such applications. Although CO2 shows poor thermodynamic properties with reference to the energy efficiency of a traditional inverse cycle, it is seen as an effective solution to the problem of the global warming of anthropic origin, since its ODP is zero and its GWP is negligible, even zero, if the fluid is recovered from waste of industrial processes. Of course, energy efficiency is an essential requirement of every substitute for traditional refrigerants; this means that CO2 could meet with success only on condition that a more sophisticated cycle and/or more energy effective components compensate for lower energy efficiency of the reference cycle. In this paper different thermodynamic inverse cycles are investigated and the related coefficients of performance (COP) values are compared. Because of its low critical temperature, the inverse cycle is different from a traditional one and often is ‘‘transcritical’’: i. e., the upper pressure is higher than the critical one and heat transfer does not involve phase transformation (condensation) but only gas cooling (consequently the heat exchanger is named gas cooler). A transcritical cycle behaves differently from a traditional one, especially with reference to the function of the throttling valve and its operation. Many Authors have dealt with these topics, but the contributions of Cavallini and Neksa˚ (2001), Neksa˚ (2002), Groll (2001), Lorentzen (1994), Cecchinato et al. (2005), Kim et al. (2004) and Sievers (2005), appear to deserve a mention within the scope of the present paper.
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Subscripts 1s first stage compressor 2s second stage compressor A auxiliary cycle compressor (in DTAC) E evaporator e external cooling agent G gas cooler I intermediate i inlet is isentropic M main cycle compressor (in DTAC) o outlet
2.
The investigated cycles
In the present study different cycles are investigated. They implement traditional methods of reducing the exergy losses during throttling and compression, i.e. two-stage throttling and inter-refrigeration of the vapour at the intermediate pressure of two-stage compression, accomplished by heat rejection to an external cooling agent, through an InterCooling Heat exchanger (ICHX). Similar thermodynamic cycles are investigated in the open literature, Huff et al. (2002), Baek et al. (2002), Minetto et al. (2005). The following cycles are investigated: 1) Single-Throttling, Single-Compression (STSC): the basic cycle with a single-throttling valve and a single compressor. This cycle is performed by a refrigerating circuit similar to the one shown in Fig. 1, except for substituting a single-stage compression for the two-stage compression here represented. 2) Single-Throttling, Double-Compression (STDC): the cycle with a single-throttling valve and two-stage compression with inter-cooling of the vapour at the intermediate pressure, as in Fig. 1.
Fig. 1 – Single-Throttling, Double-Compression Cycle (STDC).
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3) Double-Throttling, Double-Compression, Split Cycle (DTDC_SC): the cycle represented in Fig. 2a and b. The high pressure fluid after the gas cooler is split into two streams; one of them is throttled down to the intermediate pressure and is used to cool the residual stream of high pressure gas, before the throttling valve that feeds the evaporator. 4) Double-Throttling, Double-Compression, Open Flash Tank (DTDC_OFT): the cycle represented in Fig. 3a and b. The high pressure gas after the gas cooler is throttled down to the intermediate pressure and enters a vessel (OFT) from which the vapour is sucked by the high pressure compressor; the stream of the vapour produced by flashing is used to cool the high pressure gas exiting from the gas cooler. The liquid collected inside the open flash tank is throttled down to the evaporation pressure. 5) Double-Throttling, Auxiliary Compressor Cycle (DTAC): the refrigerating circuit performing this cycle is represented in
Fig. 3 – Double-Throttling, Double-Compression, open Flash tank Cycle (DTDC_OFT) and p–h diagram.
Fig. 4. After the gas cooler, the gas undergoes a further cooling process, provided by an auxiliary circuit, using an Internal Secondary Heat exchanger (ISHX). The gas is then throttled down to the evaporation pressure. All the investigated cycles, except the Double-Throttling, Auxiliary Compressor Cycle (DTAC) include an internal heat exchanger (IHX) between the line of high pressure fluid (gas or liquid) going to main throttling valve (the one before the evaporator) and the vapour line before the compressor. The above cycles were theoretically investigated using an original simulation code under the following assumptions:
Fig. 2 – Double-Throttling, Double-Compression, Split Cycle (DTDC_SC) and p–h diagram.
1) Saturated vapour at the evaporator outlet. 2) No superheating at ISHX of the DTAC cycle, at the evaporation side. 3) Temperature approach at gas cooler, at ICHX, IHX and ISHX heat exchangers ¼ 3 C. For gas cooler and ICHX the same
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The variables subjected to optimisation depend on the considered cycle. It is well known that in transcritical inverse cycles the upper pressure is not any more linked to the temperature of the heat rejection, but it is an independent variable to be optimised: as a matter of fact, if the refrigerant temperature at the gas cooler outlet is constant, the increase in the discharge pressure brings about an increase in the compression work and, at the same time, a higher value for the refrigerating effect so as to give rise to the maximum COP for a definite value of the upper pressure. Beyond this variable, two-stage compression entails an optimal value of the intermediate pressure with respect to COP. Moreover, in the split cycle (DTDC_SC) it is possible to freely choose another variable, the ratio c of the mass flow rate throttled down to the intermediate pressure to the flow rate feeding the evaporator. In fact the condition of a definite approach temperature inside
Fig. 4 – Double-Throttling, Auxiliary Compressor Vapour Cycle (DTAC).
external cooling agent was considered; its flow rate was supposed large enough to realise the closest approach between the fluids flowing inside heat exchangers at the cold end. 4) The overall isentropic compressor efficiency his depends on the compression ratio, according to the diagram in Fig. 5. Two different curves are assumed, depending on the compressor suction pressure. Curve (a), in Fig. 5, is applied whenever suction pressure is higher than 2 MPa, while curve (b) is used if suction pressure is lower than 2 MPa. Curve (a) is derived from a combination of experimental data (Bernabei et al., 2008) and catalogue data (Dorin, 2007) of reciprocating semi-hermetic compressors for transcritical applications. Curve (b) is interpolated from catalogue data of reciprocating semi-hermetic compressors for subcritical applications (Bitzer, 2004). Overall isentropic compressor efficiency includes the electric losses of the motor.
Fig. 5 – Overall isentropic efficiency as a function of pressure ratio for evaporation pressure higher (a) and lower (b) than 2 MPa.
Fig. 6 – COP of a STSC and a STDC cycle, with and without IHX, at TE [ 4 8C (a), L10 8C (b), L30 8C (c).
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Fig. 7 – COP of different cycles with IHX and ICHX, at different upper pressures, at TE [ 4 8C. Note that STDC and DTDC_SC curves are nearly coincident for intermediate pressure above the transcritical one.
the High Pressure Internal Heat exchanger (HPIHX) is not sufficient to determine this flow rate ratio. It follows that the optimal subdivision of the main stream has to be determined. This optimisation has to be carried out considering that the specific heat of the fluid varies as a function of temperature. In the case of the auxiliary compressor cycle (DTAC), the optimisation process involves the evaporation pressure of the secondary cycle instead of the intermediate pressure, as well as the high pressure of both circuits. The evaporation pressure of the secondary cycle determines the mass flow ratio _ M Þ required to match the specified approach at _ A =m c ¼ ðm ISHX. For all the considered cycles, except DTAC, a generalized form of the system coefficient of performance can be written as: ho;E hi;E (1) COP ¼ ho;1s hi;1s þ ð1 þ cÞ ho;2s hi;2s For the DTAC, it can be written as:
COP ¼
ho;E hi;E ho;M hi;M þ c ho;A hi;A
(2)
With the considered assumptions and being fixed the values of evaporation and external cooling agent temperatures, from equation (1) the dependence of the COP from the independent variables can be easily written: COP ¼ f pG ; pI ; c
(3)
where the c ratio and pG,A must be considered independent variables only for DTDC_SC and DTAC cycle respectively, thus reducing the problem of finding the optimum values of the independent variables to the solution of a multi-variable rootfinding problem of a nonlinear equation. In the simulation code a Broyden’s method was applied. The refrigerant properties are computed by interpolation from the points of a suitable database that was previously generated through the code REFPROP 7.0 (Lemmon et al., 2002).
3.
Analysis of the results
Two-stage compression and two-stage throttling are widely employed with traditional inverse cycles as means for improving energy efficiency; the improvement results mainly from a reduction of the exergy losses during throttling often combined with an increase in isentropic efficiency of the compression, as a consequence of reduced pressure ratio; another significant advantage is present in transcritical cycles, related to inter-stage cooling with external heat rejection. This practice in traditional cycles is seldom used, since the temperature of the compressed vapour at the intermediate pressure is rather low and therefore does not allow significant heat rejection to the outside environment, but in transcritical CO2 cycles the superheating of the compressed vapour is far higher and for that reason external heat rejection is often effective in reducing compression work. In the diagrams of Fig. 6 the performance of STSC and STDC cycles are compared at þ4, 10 and 30 C evaporation temperature and 30 C external cooling agent temperature. These two cycles are different only for the compression process (single-stage and two-stage with inter-stage cooling) and the gain in COP is a consequence mainly of the inter-stage heat rejection, although also the modified pressure ratios have an effect on the isentropic compression efficiency. Of course, the intermediate pressure has a strong influence on intercooling and on the resulting COP and must be optimised: COP data in Fig. 6 concerning two-stage compression refer to intermediate pressure leading to maximum COP. Inter-stage heat rejection depends heavily on the presence of the internal heat exchanger IHX and on its effectiveness: to clarify this point in Fig. 6, in addition to the data referring to STSC and STDC cycles, the corresponding data obtained without IHX are shown. The obvious conclusion is that the internal heat exchange between vapour at low pressure and the high pressure fluid before throttling enhances the benefit of inter-stage heat rejection.
international journal of refrigeration 32 (2009) 1058–1067
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Fig. 8 – Effect of heat exchange (IHX and ICHX) and double throttling on COP at different upper pressures, at TE [ 4 8C. The role played by upper and intermediate pressure in energy efficiency is illustrated in Fig. 7 at þ4 C evaporation temperature and 30 C external cooling agent temperature. For low intermediate pressures, no significant improvement appears from using more sophisticated cycles than STDC, except DTAC cycle. In this specific situation DTAC performs better than the other cycles because the pressure ratios of both compressors allow higher values of isentropic efficiency. When the intermediate pressure increases beyond a definite limit the trend line of COP for DTDC_SC and DTDC_OFT cycles changes and a growing advantage appears; the reason lies on the fact that the temperature of the compressed gas at the intermediate pressure enables interstage cooling; COP increases up to its maximum value and then decreases when the compression work of the upper stage becomes too small in comparison with that of the lower stage. The behaviour of STDC and DTDC_SC cycles when the intermediate pressure is higher than the critical one is fully described in Section 3.1. In Fig. 8 the curves of STDC and DTDC_OFT cycles with or without IHX and ICHX are plotted with the purpose of separating the effects of heat exchange from those resulting from double throttling. The conclusion is that for transcritical CO2 cycles, unlike for the traditional application of two-stage inverse cycles, energy saving resulting from inter-stage cooling during compression is even more important than the one resulting from staged throttling.
3.1.
In order to investigate the Plank cycle efficiency and the peculiar shape of its efficiency curve a simple theoretical STDC cycle was simulated. It is worth noting that when the intermediate pressure level is higher than the critical one, STDC and DTDC_SC systems show very similar performances, because no evaporation can occur in the HPIHX of the DTDC_SC system and the heat exchanged between the two streams is almost negligible (see Fig. 7). To better point out the phenomenon the following assumptions were made:
Consideration on the Plank cycle
As it can be easily noticed in Fig. 7 for STDC and DTDC_SC systems, when, increasing intermediate pressure, the transcritical cycle converts into the so-called Plank cycle (Plank, 1912), a sharp maximum in the COP curve can be observed; this phenomenon is known and was already outlined by Inokuty (1924). Plank cycles are characterised by intermediate pressure values higher than the critical pressure, thus reducing the volumetric capacity of the second stage, which is fed by an high density gas and the mechanical energy needed for this compression.
Fig. 9 – Theoretical COP of STDC cycle, at different upper pressures (a) and at different outlet intercooler temperature (b), at TE [ 4 8C.
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1) evaporation temperature is set at 4 C in order to reduce the fraction of first stage compression work on the overall compression work; 2) internal heat exchanger (IHX) is not included in the cycle to simplify the investigation of the problem; 3) overall isentropic compressor efficiency is considered unitary (his ¼ 1) to avoid masking effect due to compressor variable efficiency. In Fig. 9a COP is plotted against intermediate pressure for four different upper pressure levels ( pG ¼ 10, 12, 15 MPa) at the same external cooling agent temperature of 30 C while, in Fig. 9b, three values of this last variable were considered (Te ¼ 30, 33, 36 C) at the same upper pressure of 12 MPa. It appears that at the same external cooling agent temperature, the intermediate pressure level corresponding to the maximum efficiency is not strongly sensitive to upper pressure variations, whereas the effect of the cooling agent temperature is remarkable, being constant the upper pressure. Keeping constant the upper pressure value, and thus the refrigerating capacity for a set external cooling agent temperature, the COP maximisation problem for the STDC cycle reduces to the minimisation of the mechanical compression specific work that can be expressed as: (4) L ¼ ho;1s hi;1s þ ho;2s hi;2s
Keeping in mind that the term ðvh=vpÞs jo;E in equation (5) is not dependent on pI, the first term of equation (6) is null, while the second term is constant, not depending on upper or intermediate pressure values; equation (6) therefore can be rewritten as follows, being the constant equal to ðvh=vpÞs jo;E : " # dL d vh vh pG pI ¼ þconst: ¼ 0 (7) dpI dpI vp s o;I vp s o;I To understand the trends of the curves in Fig. 9 it is useful to observe how the derivative dL=dpI depends on pI. This derivative is composed of 3 terms, according to equation (7); in Fig. 11 the curves representing the first term and the sum of the last terms are plotted. While the sum of the last terms is subjected to rather small variations as the intermediate pressure pI change, the first term is a strong function of pI. In particular this curve presents always a negative value and shows in general a rising profile, interrupt by a sharp and deep depression. The derivative of the total work with respect to pI
where the subscripts refer to the points in Fig. 10. Considering h as function of p and s, in the pressure range of interest the partial derivative of enthalpy with respect to pressure at constant entropy ðvh=vpÞs is nearly constant along an isentropic line, therefore equation (4) can be written as: vh vh p p þ pG pI (5) L¼ I E vp s o;E vp s o;I The minimum of the compression specific work can be now calculated, finding the zero of the partial derivative of equation (5) with respect to the intermediate pressure pI, under the constrain of constant To,I temperature. " # " # dL d vh vh d vh p ¼ p þ þ I E dpI dpI vp s o;E vp s o;E dpI vp s o;I vh pG pI ¼0 ð6Þ vp s o;I
Fig. 10 – p–h diagram of a two-stage compression for a transcritical intermediate pressure.
Fig. 11 – Derivative of the mechanical specific work (equation (7)), at pG [ 10 MPa (a), 12 MPa (b), 15 MPa (c).
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follows the shape of the first term, that is only slightly lifted by the sum of the last terms. Keeping in mind that the trends of work and COP are opposite, it follows that a sharp fall of the derivative means a sharp increase in COP; this happens at a value of pI close to 7.70 MPa for Te ¼ 30 C, irrespective of the value of the upper pressure of the cycle and the maximum value of COP is just after the sharp increase, since immediately the derivative of the total work cross the axis of abscissas. The reason why the first term of equation (7) behaves in such a way can be traced to the shape of the isotherms in the p–h diagram of CO2 in the near-critical region (see Fig. 10); it is clear that, when the slope of the isothermal line corresponding to To,I flattens and is close to an horizontal line, the derivative in the first term of equation (7), which has always a negative value, increases much in modulus; for the critical isotherm the slope becomes horizontal and the modulus of the derivative is infinite. For the isothermal lines above the critical one, the peak of the derivative occurs close to the flex of each line. It is now interesting to weigh the influence of the upper pressure value in the determination of the intermediate pressure that minimizes the mechanical compression specific work; an analysis of each term and of the whole equation was carried out. Keeping constant the cooling agent temperature at 30 C, different levels of upper pressure (10, 12, 15 MPa) were considered. The equation values have been evaluated with a 0.01 MPa step, approximating the derivative to a Newton quotient with a 10 Pa pressure step. The results are shown in Fig. 11a–c where the minimum compression work associated to the Plank cycle corresponds to the zero of the bold solid line. The optimal intermediate pressure values for the Plank cycle corresponds to 7.77, 7.82, 7.86 MPa for upper pressure of 10, 12, 15 MPa respectively. As it was also observed for Fig. 9a, the optimal intermediate pressure is not strongly affected by upper pressure variations, this is due to the shape of the first term of equation (7), represented by a thin solid line in Fig. 10a–d. This term has a sharp minimum value corresponding to 7.71 MPa that depends only on TI, and it is therefore independent from the upper pressure level. In fact, the pressure difference ( pGpI) only affects the magnitude of the first term in equation (7), but not the pI value of the minimum. Therefore, due to the very narrow pI range, where the sharp variation occurs, the pressure value that optimizes the COP, remains nearly constant (less than 2.0% of variation for a pG ranging from 10 to 15 MPa) varying pG.
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Fig. 12 – COP of different cycles, as a function of different external cooling agent temperature, at TE [ L30 8C (a), L10 8C (b). Note that DTDC_OFT and DTDC_SC curves are nearly coincident at TE [ L30 8C.
range from þ25 to þ35 C, and for air conditioning the range was extended up to 50 C, with reference to automotive applications; the fluid temperature at the gas cooler outlet is assumed 3 C higher than the temperature of the external cooling agent. It is worth reminding that the same assumptions made in Section 2 about evaporator superheating, internal heat exchanger approach and overall isentropic compression efficiency are kept. The COP values of the investigated cycles are shown in Figs. 12 and 13, respectively for retail refrigeration and air conditioning, as functions of the temperature of the external
4. Comparison of cycles in terms of energy efficiency The five cycles depicted in Section 2 are analysed with reference to the typical working conditions of: 1) Retail refrigeration of frozen foodstuffs: TE ¼ 30 C. 2) Retail refrigeration of fresh foodstuffs: TE ¼ 10 C. 3) Air conditioning: TE ¼ þ4 C. Please note that for technological constraints, STSC and DTAC cycles are unsuitable for the first working condition. The temperature of the external cooling agent was varied in the
Fig. 13 – COP of different cycles, as a function of different external cooling agent temperature, at TE [ 4 8C.
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The single-stage cycle coupled with a gas cooling circuit (DTAC) shows a 17.3% increase in energy efficiency in comparison with the basic single-stage (STSC) cycle at 10 C evaporation temperature, exceeding also the single-throttling, double-compression (STDC) cycle. As it can be seen in Fig. 13, at þ4 C evaporation temperature, its performance fades when external cooling agent temperature raises.
5.
Fig. 14 – Upper pressure, intermediate pressure and mass flow ratio of different cycles, as functions of different external cooling agent temperature, at TE [ L30 8C (a), L10 8C (b). Note that DTDC_OFT and DTDC_SC curves are nearly coincident at TE [ L30 8C.
cooling agent (Te). The optimised values of the upper cycle pressure ( pG) and of the intermediate pressure ( pI) for DTDC_SC, DTDC_OFT and DTAC cycles are shown in Figs. 14 and 15; the mass flow ratio c is also displayed (for DTCC_SC is the optimal one). For every working condition, it results that the split (DTDC_SC) and the phase separation (DTDC_OFT) cycles outperform all other options, showing 20.6 and 16.8% average increase respectively in energy efficiency over the STSC cycle at þ4 C evaporation temperature, 29.3 and 28.7% increase respectively at 10 C. At 30 C, where STSC cycle is hardly advisable, the increase over the STDC cycle is of 15.6 and 15.7% respectively.
Fig. 15 – Upper pressure, intermediate pressure and mass flow ratio of different cycles, as functions of different external cooling agent temperature, at TE [ 4 8C.
Conclusions
It is well known that the theoretical transcritical inverse cycle operated on carbon dioxide involves a penalisation in energy efficiency in comparison with the traditional vapour compression cycles. However the favourable characteristics of this fluid concerning heat transfer, pressure drop and probably the compression process in a real system can partially compensate for this intrinsic thermodynamic penalisation. On the other hand, energy efficiency is an essential requirement for complying with the regulations dictated by the environmental emergency concerning global warming; thus the need of more sophisticated cycles to overcome the thermodynamic disadvantage. As the traditional compression vapour inverse cycle, exergy losses during throttling and gas cooling process are responsible for low energy efficiency; the remedies are the same, namely, staged throttling, or strong cooling of the fluid before the expansion, and staged compression with inter-cooling. The analysis performed in this study has shown that, unlike traditional cycle, staged compression with inter-cooling carried out with an external fluid for the heat rejection plays a major role in improving energy efficiency. Since this heat rejection depends heavily on the value of the intermediate pressure, the optimal value of this parameter is a crucial choice; for the same reason, an effective heat exchanger between the suction line and the line before the throttling valve often allows a significant benefit in energy efficiency. Different cycles are analysed and optimised in this paper. As expected, the most elaborate cycles (Double-Throttling, Double-Compression in both versions Open Flash Tank and Split Cycle) present the greatest improvement, especially for the heaviest operating conditions (the lowest evaporating temperature and the highest external temperature); for 30/ þ35 C (evaporation temperature/external temperature) both cycles behave similarly and give rise to 70% increase in energy efficiency against the simplest solution (Single- Throttling, Single-Compression). Being the double-compression mandatory for limiting the temperature at the compressor outlet in such conditions, the only alternative is Single-Throttling, Double-Compression (roughly 50% increase in energy efficiency). The final choice therefore results from the best trade-off between increased installation costs and decreased operating costs, taking into account also the reliability and the safety characteristics of the system. For less severe operating conditions, probably a cheaper system design can be preferable; for example at þ4/þ30 C operations, the best cycles (again DTDC_OFT and DTDC_SC) improve energy efficiency by 16% against the cheapest solution (STSC), while the system with an auxiliary compressor
international journal of refrigeration 32 (2009) 1058–1067
(DTAC) is quoted for 12% improvement. Since the last system is rather simple, reliable and cost effective, this solution is worth considering. The Plank cycle (staged compression with intermediate pressure above the critical one) could be the optimal choice only for very high value of the external cooling agent temperature and, thus, of the optimal upper pressure. A thermodynamic analysis of this cycle has been proposed to fill a gap in the knowledge of the possibility of transcritical cycles. As follows from the results of the present analysis, it is not always easy to choose the best system for a definite application and this problem is often complicated by the need of finding the optimal values for one or two independent operating variables: a reliable simulation model to be used as an optimisation tool is mandatory. In this work a merely thermodynamic optimisation of different cycle was performed. In order to turn into reality the suggestions arising from the present analysis, technological solutions are needed for controlling the cycle parameters and for keeping them at the optimal values; this is not a simple task, especially when searching for a good cost/benefit ratio. This further analysis is beyond the scope of this paper; however it is worth noting that, while the control of the upper cycle pressure is rather easily accomplished by a proper action of a back-pressure throttling valve, the value of the intermediate pressure for staged compression depends on the swept volume ratio between the compressors and needs to be controlled by variable-frequency drive or other means; moreover the thermodynamic optimisation of DTDC_SC cycle entails a suitable control on the auxiliary throttling valve and the optimisation of DTAC cycle requires to control the swept volumes of the two compressors.
references
Baek, J., Groll, E., Lawless, P., 2002. Effect of pressure ratio across compressors on the performance of the transcritical carbon dioxide cycle with two-stage compression and intercooling. In: Proc. 2002 9th Int. Refrigeration Conf. at Purdue, Purdue Univ., USA. Bernabei, M., Cecchinato, L., Chiarello, M., Corradi, M., Fornasieri, E., 2008. Design and experimental analysis of a carbon dioxide
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transcritical chiller. In: Proceedings of the 8th IIR-Gustav Lorentzen Conference on Natural Working Fluids (GL2008). September 7–10, Copenhagen, Denmark. Bitzer, 2004. Semi-hermetic CO2 compressors Octagon K Series KP-120–1. www.bitzer.de. Cavallini, A., Neksa˚, P., 2001. Prospects for the return of CO2 as a refrigerant. In: Proceedings VI Congreso Iberoamericano de Aire Acondicionado y Refrigeracio´n. CIAR, Buenos Aires, Argentina, pp. 761–790. Cecchinato, L., Corradi, M., Fornasieri, E., Zilio C., 2005. Thermodynamic analysis of different two-stage transcritical carbon dioxide cycles. In: Proc. IIR Int. Conf. on Thermophysical Properties and Transfer Processes of Refrigerants, Vicenza, Italy. Dorin, 2007. CO2 range. www.dorin.com. Groll, E.A., 2001. Review of recent research on the use of CO2 for air conditioning and refrigeration. In: Proceedings Clima, 2000, Napoli, Italy. Huff, H.J., Hwang, Y., Radermacher, R., 2002. Options for a twostage transcritical carbon dioxide cycle. In: 5th IIR Gustav Lorentzen Conference on Natural Working Fluids, Guangzhou. Inokuty, H., 1924. Theory and experiments on vapour compression refrigerating machine with some modified cycles. Journal of the Society of Mechanical Engineers, Japan 27 (90), 876–911. Kim, M.H., Pettersen, J., Bullard, C.W., 2004. Fundamental process and system design issues in CO2 vapor compression systems. Progress in Energy and Combustion Science 30 (2), 1119–1174. Lemmon, E.W., McLinden, M.O., Huber, M.L., 2002. NIST Reference Fluid Thermodynamic and Transport Properties Refprop 7.0, NIST Std. Database. Lorentzen, G., 1994. Revival of carbon dioxide as a refrigerant. Int. J. Refrigeration 17 (5), 292–301. Minetto, S., Cecchinato, L., Corradi, M., Fornasieri, E., Zilio, C., Schiavon, A., 2005. Theoretical and experimental analysis of a CO2 refrigerating cycle with two-stage throttling and suction of the flash vapour by an auxiliary compressor. In: Proc. IIR Int. Conf. on Thermophysical Properties and Transfer Processes of Refrigerants, Vicenza, Italy. Neksa˚, P., 2002. CO2 heat pump systems. Int. J. Refrigeration 25 (4), 421–427. Plank, R., 1912. Arbeitsverfahren an Kompressionska¨ltemaschinen, insbesondere fu¨r Ka¨ltetra¨ger mit tiefer kritischer Temperatur, German Patent No. DE278095. Sievers, U., 2005. Thermodynamic Process Calculations for CO2 Refrigeration Plants with Two-Stage Compression. In: Proc. IIR Int. Conf. on Thermophysical Properties and Transfer Processes of Refrigerants, Vicenza, Italy.
available at www.sciencedirect.com
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journal homepage: www.elsevier.com/locate/ijrefrig
Thermodynamic analysis of different two-stage transcritical carbon dioxide cycles Luca Cecchinato*, Manuel Chiarello, Marco Corradi, Ezio Fornasieri, Silvia Minetto, Paolo Stringari, Claudio Zilio Dipartimento di Fisica Tecnica, Universita` di Padova, via Venezia 1, I-35131 Padova, Italy
article info
abstract
Article history:
The aim of this paper is the thermodynamic evaluation and optimisation of different two-
Received 5 February 2008
stage transcritical carbon dioxide cycles. Five different cycles are studied: basic single-
Received in revised form
stage cycle, single-throttling with two-stage compression cycle, split cycle, phase
19 August 2008
separation cycle and single-stage cycle coupled with a gas cooling circuit. Each basic cycle
Accepted 5 October 2008
is analysed for the effect of internal heat transfer between different streams of refrigerants.
Published online 1 November 2008
In the case of two-stage compression, intermediate cooling between the compressor stages is present. An analysis on the Plank cycle for intermediate pressure higher than critical one
Keywords:
is performed. Each cycle is optimised with regards to energy performance, calculating the
Refrigeration system
optimal values of both the upper and the intermediate pressures. In the case of split cycle,
Carbon dioxide
the ratio of the mass flow rate in the main stream to the one in the auxiliary stream is also
Transcritical cycle
optimised.
Comparison
ª 2008 Elsevier Ltd and IIR. All rights reserved.
Thermodynamic cycle Single-stage system Two-stage system Calculation Performance Optimization
Analyse thermodynamique de plusieurs cycles au dioxyde de carbone transcritiques bie´tage´s Mots cle´s : Syste´me frigorifique ; Dioxyde de carbone ; Cycle transcritique ; Cycle thermodynamique ; Syste´me monoe´tage´ ; Syste´me bie´tage´ ; Calcul ; Performance ; Comparison ; Optimisation
* Corresponding author. Tel.: þ39 049 827 6876; fax: þ39 049 827 6896. E-mail address: [email protected] (L. Cecchinato). 0140-7007/$ – see front matter ª 2008 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2008.10.001
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Nomenclature COP h L _ m n p Q s T x
1.
Q/L, coefficient of performance [-] enthalpy [J kg1] specific mechanical energy [J kg1] mass flow rate [kg s1] overall compression efficiency [-] pressure [Pa] specific refrigeration capacity [J kg1] entropy [J K1 kg1] temperature [ C] mass flow ratio [-]
Introduction
Carbon dioxide is one of the oldest refrigerants, as it was already employed at the end of the nineteenth century, mainly where safety was essential. However, when, around 1931, synthetic refrigerants came into use, CO2 began its decline, because the new fluids provided best energy efficiency with cheaper and more reliable equipment. High critical pressure (7.38 MPa) and rather low critical temperature (31.06 C) summarise the main drawbacks of carbon dioxide. Nevertheless today CO2 is gaining more and more favour thanks to its very low environmental impact. In 1994 the Norwegian professor Gustav Lorentzen first proposed again this refrigerant as a working fluid for vapour compression inverse cycles and from that moment many other Authors have extensively studied such applications. Although CO2 shows poor thermodynamic properties with reference to the energy efficiency of a traditional inverse cycle, it is seen as an effective solution to the problem of the global warming of anthropic origin, since its ODP is zero and its GWP is negligible, even zero, if the fluid is recovered from waste of industrial processes. Of course, energy efficiency is an essential requirement of every substitute for traditional refrigerants; this means that CO2 could meet with success only on condition that a more sophisticated cycle and/or more energy effective components compensate for lower energy efficiency of the reference cycle. In this paper different thermodynamic inverse cycles are investigated and the related coefficients of performance (COP) values are compared. Because of its low critical temperature, the inverse cycle is different from a traditional one and often is ‘‘transcritical’’: i. e., the upper pressure is higher than the critical one and heat transfer does not involve phase transformation (condensation) but only gas cooling (consequently the heat exchanger is named gas cooler). A transcritical cycle behaves differently from a traditional one, especially with reference to the function of the throttling valve and its operation. Many Authors have dealt with these topics, but the contributions of Cavallini and Neksa˚ (2001), Neksa˚ (2002), Groll (2001), Lorentzen (1994), Cecchinato et al. (2005), Kim et al. (2004) and Sievers (2005), appear to deserve a mention within the scope of the present paper.
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Subscripts 1s first stage compressor 2s second stage compressor A auxiliary cycle compressor (in DTAC) E evaporator e external cooling agent G gas cooler I intermediate i inlet is isentropic M main cycle compressor (in DTAC) o outlet
2.
The investigated cycles
In the present study different cycles are investigated. They implement traditional methods of reducing the exergy losses during throttling and compression, i.e. two-stage throttling and inter-refrigeration of the vapour at the intermediate pressure of two-stage compression, accomplished by heat rejection to an external cooling agent, through an InterCooling Heat exchanger (ICHX). Similar thermodynamic cycles are investigated in the open literature, Huff et al. (2002), Baek et al. (2002), Minetto et al. (2005). The following cycles are investigated: 1) Single-Throttling, Single-Compression (STSC): the basic cycle with a single-throttling valve and a single compressor. This cycle is performed by a refrigerating circuit similar to the one shown in Fig. 1, except for substituting a single-stage compression for the two-stage compression here represented. 2) Single-Throttling, Double-Compression (STDC): the cycle with a single-throttling valve and two-stage compression with inter-cooling of the vapour at the intermediate pressure, as in Fig. 1.
Fig. 1 – Single-Throttling, Double-Compression Cycle (STDC).
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3) Double-Throttling, Double-Compression, Split Cycle (DTDC_SC): the cycle represented in Fig. 2a and b. The high pressure fluid after the gas cooler is split into two streams; one of them is throttled down to the intermediate pressure and is used to cool the residual stream of high pressure gas, before the throttling valve that feeds the evaporator. 4) Double-Throttling, Double-Compression, Open Flash Tank (DTDC_OFT): the cycle represented in Fig. 3a and b. The high pressure gas after the gas cooler is throttled down to the intermediate pressure and enters a vessel (OFT) from which the vapour is sucked by the high pressure compressor; the stream of the vapour produced by flashing is used to cool the high pressure gas exiting from the gas cooler. The liquid collected inside the open flash tank is throttled down to the evaporation pressure. 5) Double-Throttling, Auxiliary Compressor Cycle (DTAC): the refrigerating circuit performing this cycle is represented in
Fig. 3 – Double-Throttling, Double-Compression, open Flash tank Cycle (DTDC_OFT) and p–h diagram.
Fig. 4. After the gas cooler, the gas undergoes a further cooling process, provided by an auxiliary circuit, using an Internal Secondary Heat exchanger (ISHX). The gas is then throttled down to the evaporation pressure. All the investigated cycles, except the Double-Throttling, Auxiliary Compressor Cycle (DTAC) include an internal heat exchanger (IHX) between the line of high pressure fluid (gas or liquid) going to main throttling valve (the one before the evaporator) and the vapour line before the compressor. The above cycles were theoretically investigated using an original simulation code under the following assumptions:
Fig. 2 – Double-Throttling, Double-Compression, Split Cycle (DTDC_SC) and p–h diagram.
1) Saturated vapour at the evaporator outlet. 2) No superheating at ISHX of the DTAC cycle, at the evaporation side. 3) Temperature approach at gas cooler, at ICHX, IHX and ISHX heat exchangers ¼ 3 C. For gas cooler and ICHX the same
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The variables subjected to optimisation depend on the considered cycle. It is well known that in transcritical inverse cycles the upper pressure is not any more linked to the temperature of the heat rejection, but it is an independent variable to be optimised: as a matter of fact, if the refrigerant temperature at the gas cooler outlet is constant, the increase in the discharge pressure brings about an increase in the compression work and, at the same time, a higher value for the refrigerating effect so as to give rise to the maximum COP for a definite value of the upper pressure. Beyond this variable, two-stage compression entails an optimal value of the intermediate pressure with respect to COP. Moreover, in the split cycle (DTDC_SC) it is possible to freely choose another variable, the ratio c of the mass flow rate throttled down to the intermediate pressure to the flow rate feeding the evaporator. In fact the condition of a definite approach temperature inside
Fig. 4 – Double-Throttling, Auxiliary Compressor Vapour Cycle (DTAC).
external cooling agent was considered; its flow rate was supposed large enough to realise the closest approach between the fluids flowing inside heat exchangers at the cold end. 4) The overall isentropic compressor efficiency his depends on the compression ratio, according to the diagram in Fig. 5. Two different curves are assumed, depending on the compressor suction pressure. Curve (a), in Fig. 5, is applied whenever suction pressure is higher than 2 MPa, while curve (b) is used if suction pressure is lower than 2 MPa. Curve (a) is derived from a combination of experimental data (Bernabei et al., 2008) and catalogue data (Dorin, 2007) of reciprocating semi-hermetic compressors for transcritical applications. Curve (b) is interpolated from catalogue data of reciprocating semi-hermetic compressors for subcritical applications (Bitzer, 2004). Overall isentropic compressor efficiency includes the electric losses of the motor.
Fig. 5 – Overall isentropic efficiency as a function of pressure ratio for evaporation pressure higher (a) and lower (b) than 2 MPa.
Fig. 6 – COP of a STSC and a STDC cycle, with and without IHX, at TE [ 4 8C (a), L10 8C (b), L30 8C (c).
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Fig. 7 – COP of different cycles with IHX and ICHX, at different upper pressures, at TE [ 4 8C. Note that STDC and DTDC_SC curves are nearly coincident for intermediate pressure above the transcritical one.
the High Pressure Internal Heat exchanger (HPIHX) is not sufficient to determine this flow rate ratio. It follows that the optimal subdivision of the main stream has to be determined. This optimisation has to be carried out considering that the specific heat of the fluid varies as a function of temperature. In the case of the auxiliary compressor cycle (DTAC), the optimisation process involves the evaporation pressure of the secondary cycle instead of the intermediate pressure, as well as the high pressure of both circuits. The evaporation pressure of the secondary cycle determines the mass flow ratio _ M Þ required to match the specified approach at _ A =m c ¼ ðm ISHX. For all the considered cycles, except DTAC, a generalized form of the system coefficient of performance can be written as: ho;E hi;E (1) COP ¼ ho;1s hi;1s þ ð1 þ cÞ ho;2s hi;2s For the DTAC, it can be written as:
COP ¼
ho;E hi;E ho;M hi;M þ c ho;A hi;A
(2)
With the considered assumptions and being fixed the values of evaporation and external cooling agent temperatures, from equation (1) the dependence of the COP from the independent variables can be easily written: COP ¼ f pG ; pI ; c
(3)
where the c ratio and pG,A must be considered independent variables only for DTDC_SC and DTAC cycle respectively, thus reducing the problem of finding the optimum values of the independent variables to the solution of a multi-variable rootfinding problem of a nonlinear equation. In the simulation code a Broyden’s method was applied. The refrigerant properties are computed by interpolation from the points of a suitable database that was previously generated through the code REFPROP 7.0 (Lemmon et al., 2002).
3.
Analysis of the results
Two-stage compression and two-stage throttling are widely employed with traditional inverse cycles as means for improving energy efficiency; the improvement results mainly from a reduction of the exergy losses during throttling often combined with an increase in isentropic efficiency of the compression, as a consequence of reduced pressure ratio; another significant advantage is present in transcritical cycles, related to inter-stage cooling with external heat rejection. This practice in traditional cycles is seldom used, since the temperature of the compressed vapour at the intermediate pressure is rather low and therefore does not allow significant heat rejection to the outside environment, but in transcritical CO2 cycles the superheating of the compressed vapour is far higher and for that reason external heat rejection is often effective in reducing compression work. In the diagrams of Fig. 6 the performance of STSC and STDC cycles are compared at þ4, 10 and 30 C evaporation temperature and 30 C external cooling agent temperature. These two cycles are different only for the compression process (single-stage and two-stage with inter-stage cooling) and the gain in COP is a consequence mainly of the inter-stage heat rejection, although also the modified pressure ratios have an effect on the isentropic compression efficiency. Of course, the intermediate pressure has a strong influence on intercooling and on the resulting COP and must be optimised: COP data in Fig. 6 concerning two-stage compression refer to intermediate pressure leading to maximum COP. Inter-stage heat rejection depends heavily on the presence of the internal heat exchanger IHX and on its effectiveness: to clarify this point in Fig. 6, in addition to the data referring to STSC and STDC cycles, the corresponding data obtained without IHX are shown. The obvious conclusion is that the internal heat exchange between vapour at low pressure and the high pressure fluid before throttling enhances the benefit of inter-stage heat rejection.
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Fig. 8 – Effect of heat exchange (IHX and ICHX) and double throttling on COP at different upper pressures, at TE [ 4 8C. The role played by upper and intermediate pressure in energy efficiency is illustrated in Fig. 7 at þ4 C evaporation temperature and 30 C external cooling agent temperature. For low intermediate pressures, no significant improvement appears from using more sophisticated cycles than STDC, except DTAC cycle. In this specific situation DTAC performs better than the other cycles because the pressure ratios of both compressors allow higher values of isentropic efficiency. When the intermediate pressure increases beyond a definite limit the trend line of COP for DTDC_SC and DTDC_OFT cycles changes and a growing advantage appears; the reason lies on the fact that the temperature of the compressed gas at the intermediate pressure enables interstage cooling; COP increases up to its maximum value and then decreases when the compression work of the upper stage becomes too small in comparison with that of the lower stage. The behaviour of STDC and DTDC_SC cycles when the intermediate pressure is higher than the critical one is fully described in Section 3.1. In Fig. 8 the curves of STDC and DTDC_OFT cycles with or without IHX and ICHX are plotted with the purpose of separating the effects of heat exchange from those resulting from double throttling. The conclusion is that for transcritical CO2 cycles, unlike for the traditional application of two-stage inverse cycles, energy saving resulting from inter-stage cooling during compression is even more important than the one resulting from staged throttling.
3.1.
In order to investigate the Plank cycle efficiency and the peculiar shape of its efficiency curve a simple theoretical STDC cycle was simulated. It is worth noting that when the intermediate pressure level is higher than the critical one, STDC and DTDC_SC systems show very similar performances, because no evaporation can occur in the HPIHX of the DTDC_SC system and the heat exchanged between the two streams is almost negligible (see Fig. 7). To better point out the phenomenon the following assumptions were made:
Consideration on the Plank cycle
As it can be easily noticed in Fig. 7 for STDC and DTDC_SC systems, when, increasing intermediate pressure, the transcritical cycle converts into the so-called Plank cycle (Plank, 1912), a sharp maximum in the COP curve can be observed; this phenomenon is known and was already outlined by Inokuty (1924). Plank cycles are characterised by intermediate pressure values higher than the critical pressure, thus reducing the volumetric capacity of the second stage, which is fed by an high density gas and the mechanical energy needed for this compression.
Fig. 9 – Theoretical COP of STDC cycle, at different upper pressures (a) and at different outlet intercooler temperature (b), at TE [ 4 8C.
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1) evaporation temperature is set at 4 C in order to reduce the fraction of first stage compression work on the overall compression work; 2) internal heat exchanger (IHX) is not included in the cycle to simplify the investigation of the problem; 3) overall isentropic compressor efficiency is considered unitary (his ¼ 1) to avoid masking effect due to compressor variable efficiency. In Fig. 9a COP is plotted against intermediate pressure for four different upper pressure levels ( pG ¼ 10, 12, 15 MPa) at the same external cooling agent temperature of 30 C while, in Fig. 9b, three values of this last variable were considered (Te ¼ 30, 33, 36 C) at the same upper pressure of 12 MPa. It appears that at the same external cooling agent temperature, the intermediate pressure level corresponding to the maximum efficiency is not strongly sensitive to upper pressure variations, whereas the effect of the cooling agent temperature is remarkable, being constant the upper pressure. Keeping constant the upper pressure value, and thus the refrigerating capacity for a set external cooling agent temperature, the COP maximisation problem for the STDC cycle reduces to the minimisation of the mechanical compression specific work that can be expressed as: (4) L ¼ ho;1s hi;1s þ ho;2s hi;2s
Keeping in mind that the term ðvh=vpÞs jo;E in equation (5) is not dependent on pI, the first term of equation (6) is null, while the second term is constant, not depending on upper or intermediate pressure values; equation (6) therefore can be rewritten as follows, being the constant equal to ðvh=vpÞs jo;E : " # dL d vh vh pG pI ¼ þconst: ¼ 0 (7) dpI dpI vp s o;I vp s o;I To understand the trends of the curves in Fig. 9 it is useful to observe how the derivative dL=dpI depends on pI. This derivative is composed of 3 terms, according to equation (7); in Fig. 11 the curves representing the first term and the sum of the last terms are plotted. While the sum of the last terms is subjected to rather small variations as the intermediate pressure pI change, the first term is a strong function of pI. In particular this curve presents always a negative value and shows in general a rising profile, interrupt by a sharp and deep depression. The derivative of the total work with respect to pI
where the subscripts refer to the points in Fig. 10. Considering h as function of p and s, in the pressure range of interest the partial derivative of enthalpy with respect to pressure at constant entropy ðvh=vpÞs is nearly constant along an isentropic line, therefore equation (4) can be written as: vh vh p p þ pG pI (5) L¼ I E vp s o;E vp s o;I The minimum of the compression specific work can be now calculated, finding the zero of the partial derivative of equation (5) with respect to the intermediate pressure pI, under the constrain of constant To,I temperature. " # " # dL d vh vh d vh p ¼ p þ þ I E dpI dpI vp s o;E vp s o;E dpI vp s o;I vh pG pI ¼0 ð6Þ vp s o;I
Fig. 10 – p–h diagram of a two-stage compression for a transcritical intermediate pressure.
Fig. 11 – Derivative of the mechanical specific work (equation (7)), at pG [ 10 MPa (a), 12 MPa (b), 15 MPa (c).
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follows the shape of the first term, that is only slightly lifted by the sum of the last terms. Keeping in mind that the trends of work and COP are opposite, it follows that a sharp fall of the derivative means a sharp increase in COP; this happens at a value of pI close to 7.70 MPa for Te ¼ 30 C, irrespective of the value of the upper pressure of the cycle and the maximum value of COP is just after the sharp increase, since immediately the derivative of the total work cross the axis of abscissas. The reason why the first term of equation (7) behaves in such a way can be traced to the shape of the isotherms in the p–h diagram of CO2 in the near-critical region (see Fig. 10); it is clear that, when the slope of the isothermal line corresponding to To,I flattens and is close to an horizontal line, the derivative in the first term of equation (7), which has always a negative value, increases much in modulus; for the critical isotherm the slope becomes horizontal and the modulus of the derivative is infinite. For the isothermal lines above the critical one, the peak of the derivative occurs close to the flex of each line. It is now interesting to weigh the influence of the upper pressure value in the determination of the intermediate pressure that minimizes the mechanical compression specific work; an analysis of each term and of the whole equation was carried out. Keeping constant the cooling agent temperature at 30 C, different levels of upper pressure (10, 12, 15 MPa) were considered. The equation values have been evaluated with a 0.01 MPa step, approximating the derivative to a Newton quotient with a 10 Pa pressure step. The results are shown in Fig. 11a–c where the minimum compression work associated to the Plank cycle corresponds to the zero of the bold solid line. The optimal intermediate pressure values for the Plank cycle corresponds to 7.77, 7.82, 7.86 MPa for upper pressure of 10, 12, 15 MPa respectively. As it was also observed for Fig. 9a, the optimal intermediate pressure is not strongly affected by upper pressure variations, this is due to the shape of the first term of equation (7), represented by a thin solid line in Fig. 10a–d. This term has a sharp minimum value corresponding to 7.71 MPa that depends only on TI, and it is therefore independent from the upper pressure level. In fact, the pressure difference ( pGpI) only affects the magnitude of the first term in equation (7), but not the pI value of the minimum. Therefore, due to the very narrow pI range, where the sharp variation occurs, the pressure value that optimizes the COP, remains nearly constant (less than 2.0% of variation for a pG ranging from 10 to 15 MPa) varying pG.
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Fig. 12 – COP of different cycles, as a function of different external cooling agent temperature, at TE [ L30 8C (a), L10 8C (b). Note that DTDC_OFT and DTDC_SC curves are nearly coincident at TE [ L30 8C.
range from þ25 to þ35 C, and for air conditioning the range was extended up to 50 C, with reference to automotive applications; the fluid temperature at the gas cooler outlet is assumed 3 C higher than the temperature of the external cooling agent. It is worth reminding that the same assumptions made in Section 2 about evaporator superheating, internal heat exchanger approach and overall isentropic compression efficiency are kept. The COP values of the investigated cycles are shown in Figs. 12 and 13, respectively for retail refrigeration and air conditioning, as functions of the temperature of the external
4. Comparison of cycles in terms of energy efficiency The five cycles depicted in Section 2 are analysed with reference to the typical working conditions of: 1) Retail refrigeration of frozen foodstuffs: TE ¼ 30 C. 2) Retail refrigeration of fresh foodstuffs: TE ¼ 10 C. 3) Air conditioning: TE ¼ þ4 C. Please note that for technological constraints, STSC and DTAC cycles are unsuitable for the first working condition. The temperature of the external cooling agent was varied in the
Fig. 13 – COP of different cycles, as a function of different external cooling agent temperature, at TE [ 4 8C.
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The single-stage cycle coupled with a gas cooling circuit (DTAC) shows a 17.3% increase in energy efficiency in comparison with the basic single-stage (STSC) cycle at 10 C evaporation temperature, exceeding also the single-throttling, double-compression (STDC) cycle. As it can be seen in Fig. 13, at þ4 C evaporation temperature, its performance fades when external cooling agent temperature raises.
5.
Fig. 14 – Upper pressure, intermediate pressure and mass flow ratio of different cycles, as functions of different external cooling agent temperature, at TE [ L30 8C (a), L10 8C (b). Note that DTDC_OFT and DTDC_SC curves are nearly coincident at TE [ L30 8C.
cooling agent (Te). The optimised values of the upper cycle pressure ( pG) and of the intermediate pressure ( pI) for DTDC_SC, DTDC_OFT and DTAC cycles are shown in Figs. 14 and 15; the mass flow ratio c is also displayed (for DTCC_SC is the optimal one). For every working condition, it results that the split (DTDC_SC) and the phase separation (DTDC_OFT) cycles outperform all other options, showing 20.6 and 16.8% average increase respectively in energy efficiency over the STSC cycle at þ4 C evaporation temperature, 29.3 and 28.7% increase respectively at 10 C. At 30 C, where STSC cycle is hardly advisable, the increase over the STDC cycle is of 15.6 and 15.7% respectively.
Fig. 15 – Upper pressure, intermediate pressure and mass flow ratio of different cycles, as functions of different external cooling agent temperature, at TE [ 4 8C.
Conclusions
It is well known that the theoretical transcritical inverse cycle operated on carbon dioxide involves a penalisation in energy efficiency in comparison with the traditional vapour compression cycles. However the favourable characteristics of this fluid concerning heat transfer, pressure drop and probably the compression process in a real system can partially compensate for this intrinsic thermodynamic penalisation. On the other hand, energy efficiency is an essential requirement for complying with the regulations dictated by the environmental emergency concerning global warming; thus the need of more sophisticated cycles to overcome the thermodynamic disadvantage. As the traditional compression vapour inverse cycle, exergy losses during throttling and gas cooling process are responsible for low energy efficiency; the remedies are the same, namely, staged throttling, or strong cooling of the fluid before the expansion, and staged compression with inter-cooling. The analysis performed in this study has shown that, unlike traditional cycle, staged compression with inter-cooling carried out with an external fluid for the heat rejection plays a major role in improving energy efficiency. Since this heat rejection depends heavily on the value of the intermediate pressure, the optimal value of this parameter is a crucial choice; for the same reason, an effective heat exchanger between the suction line and the line before the throttling valve often allows a significant benefit in energy efficiency. Different cycles are analysed and optimised in this paper. As expected, the most elaborate cycles (Double-Throttling, Double-Compression in both versions Open Flash Tank and Split Cycle) present the greatest improvement, especially for the heaviest operating conditions (the lowest evaporating temperature and the highest external temperature); for 30/ þ35 C (evaporation temperature/external temperature) both cycles behave similarly and give rise to 70% increase in energy efficiency against the simplest solution (Single- Throttling, Single-Compression). Being the double-compression mandatory for limiting the temperature at the compressor outlet in such conditions, the only alternative is Single-Throttling, Double-Compression (roughly 50% increase in energy efficiency). The final choice therefore results from the best trade-off between increased installation costs and decreased operating costs, taking into account also the reliability and the safety characteristics of the system. For less severe operating conditions, probably a cheaper system design can be preferable; for example at þ4/þ30 C operations, the best cycles (again DTDC_OFT and DTDC_SC) improve energy efficiency by 16% against the cheapest solution (STSC), while the system with an auxiliary compressor
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(DTAC) is quoted for 12% improvement. Since the last system is rather simple, reliable and cost effective, this solution is worth considering. The Plank cycle (staged compression with intermediate pressure above the critical one) could be the optimal choice only for very high value of the external cooling agent temperature and, thus, of the optimal upper pressure. A thermodynamic analysis of this cycle has been proposed to fill a gap in the knowledge of the possibility of transcritical cycles. As follows from the results of the present analysis, it is not always easy to choose the best system for a definite application and this problem is often complicated by the need of finding the optimal values for one or two independent operating variables: a reliable simulation model to be used as an optimisation tool is mandatory. In this work a merely thermodynamic optimisation of different cycle was performed. In order to turn into reality the suggestions arising from the present analysis, technological solutions are needed for controlling the cycle parameters and for keeping them at the optimal values; this is not a simple task, especially when searching for a good cost/benefit ratio. This further analysis is beyond the scope of this paper; however it is worth noting that, while the control of the upper cycle pressure is rather easily accomplished by a proper action of a back-pressure throttling valve, the value of the intermediate pressure for staged compression depends on the swept volume ratio between the compressors and needs to be controlled by variable-frequency drive or other means; moreover the thermodynamic optimisation of DTDC_SC cycle entails a suitable control on the auxiliary throttling valve and the optimisation of DTAC cycle requires to control the swept volumes of the two compressors.
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