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Optimization of ejector-expansion transcritical CO2 heat pump cycle
ARTICLE IN PRESS Energy 33 (2008) 1399– 1406
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Optimization of ejector-expansion transcritical CO2 heat pump cycle Jahar Sarkar Department of Mechanical Engineering, Institute of Technology, BHU, Varanasi 221005, India
a r t i c l e in fo
abstract
Article history: Received 28 December 2007
Optimization studies along with optimum parameter correlations, using constant area mixing model are presented in this article for ejector-expansion transcritical CO2 heat pump cycle with both conventional and modified layouts. Both the energetic and exergetic comparisons between valve, turbine and ejector-expansions-based transcritical CO2 heat pump cycles are also studied for simultaneous cooling and heating applications. Performances for conventional layouts are presented by maximum COP, optimum discharge pressure and corresponding entrainment ratio and pressure lift ratio of ejector, whereas for modified layout by maximum COP, optimum discharge pressure and corresponding pressure lift ratio. The optimization for modified layout can be realized for certain entrainment ratio, evaporator and gas cooler exit temperature combinations. Considering the trade-off between the system energetic and exergetic performances, and cost associated with expansion devices, the ejector may be the promising alternative expansion device for transcritical CO2 heat pump cycle. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Ejector-expansion CO2 cycle Modelling Entrainment ratio Pressure lift ratio Optimization Performance comparison
1. Introduction Use of ejector as an expansion device in transcritical CO2 cycle seems to be a promising modification to improve the system performance [1–3]. Kornhauser [4] analyzed the thermodynamic performance of the ejector-expansion refrigeration cycle using R12 as a refrigerant based on constant mixing pressure model and found a COP improvement of up to 21% over the standard cycle under standard operating conditions. Liu et al. [5] first performed a thermodynamic analysis of the transcritical CO2 vapor compression/ejection hybrid refrigeration cycle. Another theoretical study on transcritical CO2 systems with ejector to study the effect of internal heat exchanger on the performance was reported by Elbel et al. [6]. Use of ejector in transcritical CO2 cycle not only improve the COP, also simplifies the process of controlling the gas cooler pressure in the CO2 cycle by changing the throat area of the ejector nozzle [7]. Experiment showed that the COP of the car airconditioner using the ejector cycle increases by 20% over the conventional cycle [7]. Ejector is much more beneficial to CO2 systems with maximum COP improvement of 44% compared with R134a system of 13% for 100% isentropic ejector efficiency, however, key is to build highly efficient ejectors [2]. Li and Groll [8] recently modified the ejector-expansion cycle by allowing part of the vapor in the separator feed back to the evaporator, which regulates the quality at the evaporator inlet and through theoretical analysis, they showed the COP improvement
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to be more than 16%. Through comparative study, Deng et al. [9] showed that the ejector improves the maximum COP by up to 18.6% compared with the internal heat exchanger system and by 22.0% compared with the conventional system with greatly reducing the throttling losses. Although optimization studies for other cycle modifications have been reported in open literature [10–12], such theoretical optimization studies with ejector for simultaneous cooling and heating are scarce. The present study, on transcritical CO2 cycle for simultaneous cooling and heating, consists of three parts. The first part presents the optimization of high pressure along with entrainment ratio and pressure lift ratio based on the maximum system COP for the ejector-expansion transcritical CO2 heat pump cycle with conventional layout (CEETC) by using constant area mixing model. The second part presents the optimization of ejector-expansion transcritical CO2 heat pump cycle with modified layout (MEETC) by using constant area mixing model. The third part presents the comparison of optimum high side pressure, performances and expansion exergy loss for transcritical CO2 heat pump cycle based on three expansion devices: valve, turbine and ejector.
2. Ejector-expansion CO2 heat pump cycle layout In the present study, the compressor discharge pressure optimization to get the maximum COP has been done for two ejector-driven transcritical CO2 cycle layouts. First one is the conventional ejector-driven cycle, proposed by Kornhauser [4], which is shown in Fig. 1 and the corresponding P–h diagram is shown in Fig. 2. The primary flow from the gas cooler and the
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Nomenclature a TA COPs h P PLR q t,T T0 u w x m r Z
ZII
cross-sectional area (m2) temperature approach (K) system coefficient of performance specific enthalpy (kJ/kg) pressure (bar) pressure lift ratio specific cooling/heating effect (kJ/kg) temperature (1C, K) reference temperature (K) fluid velocity (m/s) specific work (kJ/kg) vapor quality entrainment ratio fluid density (kg/m3) isentropic efficiency
second law efficiency
Subscripts c cd d ed ej ev gc gc,out max n opt si/so
compressor compressor discharge ejector diffuser expansion device ejector evaporator gas cooler gas cooler outlet maximum ejector nozzle optimum secondary fluid inlet/outlet
secondary flow from the evaporator are passing through nozzle, mixing and diffuser sections of the ejector and then separating in forms of vapor and liquid so that this ratio should matched with the inlet ratio of primary and secondary flows. Second one is the modified ejector-driven cycle, proposed by Li and Groll [8], which is shown in Fig. 3 and the corresponding P–h diagram is shown in Fig. 4. The main difference with conventional ejector cycle is that some part of vapor from separator is feed back to evaporator through throttle valve to regulate the quality of evaporator inlet. Two ejector performance parameters significantly influence the system performance with an optimum ratio, which can be defined by [13] Entrainment ratio; m ¼
masss of secondary flow mass of primary flow
Pressure lift ratio; PLR ¼
(1)
static pressure at diffuser exit static pressure at secondary flow inlet (2)
Fig. 1. Schematic diagram of conventional ejector-expansion transcritical CO2 cycle.
3. Mathematical modeling and simulation The ejector-driven transcritical CO2 heat pump cycle for the both layouts has been modeled based on the mass, momentum and the energy conservations. To simplify the theoretical model and set up the equations per unit total ejector flow for the both cycle layouts, the following assumptions are made:
Pgc
2
Pressure
3
5
6
1 8
7 4
10
Pev
9
Specific enthalpy Fig. 2. P–h diagram of conventional ejector-expansion transcritical CO2 cycle.
(i) Neglect the pressure drop in the gas cooler and evaporator and the connection tubes. (ii) No heat transfer with the environment for the system. (iii) The refrigerant condition at the evaporator outlet is saturated. (iv) The vapor stream from the separator is saturated vapor and the liquid stream from the separator is saturated liquid. (v) The flow across the expansion valve or the throttle valves is isenthalpic. (vi) The compressor has a given isentropic efficiency. (vii) Both the motive stream and the suction stream reach the same pressure at the inlet of the constant area mixing section of the ejector. There is no mixing between the two streams before the inlet of the constant area mixing section. (viii) The expansion efficiencies of the motive stream and suction stream are given constants. The diffuser of the ejector also has a given efficiency.
ARTICLE IN PRESS J. Sarkar / Energy 33 (2008) 1399–1406
1401
And for the diffuser section the energy balance is given by h5 ¼ h10 þ u210 =2
(8)
The overall energy balance in the ejector for both cycle layouts is given by ð1 þ mÞh5 ¼ h3 þ mh8
(9)
For both cycle layouts, the specific compressor work and heating effect can be found by wc ¼
1 ðh2 h1 Þ 1þm
(10)
qgc ¼
1 ðh2 h3 Þ 1þm
(11)
For the conventional ejector cycle (Fig. 1), the specific cooling effect: Fig. 3. Schematic diagram of modified CO2 cycle with ejector-expansion device.
qev ¼
m ðh8 h6 Þ 1þm
Whereas for the modified ejector cycle (Fig. 3), m 1 h8 ð1 x5 Þh6 x5 h1 qev ¼ 1þm 1þm
Pgc
3
2
Pressure
1 8
7 4
10
Pev
9
0 Specific enthalpy Fig. 4. P–h diagram of modified ejector-expansion transcritical CO2 cycle.
(ix) Kinetic energies of the refrigerant at the ejector inlet and outlet are negligible. Based on the above assumptions, the following equations can be setup in the nozzle section of ejector for both the layouts: h3 ¼ h4 þ u24 =2
(3)
h8 ¼ h9 þ u29 =2
(4)
For given entrainment ratio, the following mass, momentum and energy equations in the constant area mixing section of ejector can be identified for both cycle layouts [8]: (5)
u10 ¼ ðu4 þ mu9 Þ=ð1 þ mÞ P 10 ða4 þ a9 Þ þ u10 ¼ P9 ða4 þ a9 Þ þ
h10 þ
2
u210 u 1 h4 þ 4 ¼ 1þm 2 2
1 m u4 þ u9 1þm 1þm
u2 m h9 þ 9 þ 1þm 2
(14)
Based on the theoretical model of ejector-driven transcritical CO2 heat pump cycles, the simulation code was developed to investigate the effect of different operating parameters for both layouts, which was integrated with the thermodynamic property code CO2PROP [10] to compute relevant thermodynamic parameters of carbon dioxide in sub- and super-critical regions. For given compressor discharge pressure, evaporator and gas cooler exit temperatures, the algorithm of code for conventional cycle is as follows:
5 11
(13)
The system COP (combined cooling and heating) can be calculated by COP s ¼ ðqev þ qgc Þ=wc
6
(12)
(6)
(7)
(i) Properties at states 8 and 3 are calculated. Enthalpies and other thermodynamic properties at states 9 and 4 are calculated by given nozzle efficiency and P8–P9. Velocities at the corresponding states are calculated by using Eqs. (3) and (4) and then areas are also calculated. (ii) Some value of entrainment ratio is assumed for iteration. (iii) Using Eqs. (5)–(7), the pressure, enthalpy and fluid velocity at exit of mixing section (state 10) are calculated by effective iteration technique, which satisfy the condition: r10(a4+a9)u10 ¼ 1 (for unit flow rate) and then other properties are calculated. (iv) Using Eqs. (9) or (8) and given diffuser efficiency, enthalpy, pressure and vapor quality at state 5 are calculated and then other properties are also calculated. (v) If the condition (1+m)x5 ¼ 1 is not satisfied, steps (iii)–(iv) will repeated by using new value of m [ ¼ (1x5)/x5] until the condition satisfied. (vi) Properties at states 6, 7 and 1 are calculated. Then the properties of state 2 are calculated using given compressor isentropic efficiency. (vii) Using Eqs. (10)–(12) and (14), the performance parameters: wc, qev, qgc and COPs are calculated and PLR ( ¼ P1/Pev) is also calculated. For the modified ejector-driven cycle simulation, similar algorithm has been used excluding iteration loop for entrainment ratio as it is user defined, i.e. steps (i), (iii)–(iv), (vi)–(vii), only qev is calculated by using Eq. (13) instead of Eq. (12) at the last step.
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In the present numerical model, following tolerances have been used for convergence in simulation for the overall satisfaction: 103 for temperature (K) and enthalpy (kJ/kg), 104 for mass flow rate (0.01% for unit mass flow rate) and 105 for entrainment ratio, which may give the error for mass balance as 0.01%, in energy balance below 0.01% and system COP computation in the range of 104. The ejector-driven transcritical CO2 cycle for combined cooling and heating applications is optimized on the basis of maximum system COP. These values are obtained for various operating conditions along with variation of the compressor discharge pressure having a step size of 0.5 bar. In general, for the CEETC and MEETC, respectively, the system COP can be expressed by COP sys ¼ f ðt ev ; t gc;out ; P 8 P 9 ; P d ; Zc ; Zn ; Zd Þ
(15)
COP sys ¼ f ðt ev ; t gc;out ; P 8 P 9 ; P d ; m; Zc ; Zn ; Zd Þ
(16)
Based on the assumptions made, the optimum discharge pressure, entrainment ratio and pressure lift ratio and maximum system COP for CEETC are expressed by P cd;opt ; COP s;max ; mopt ; PLRopt ¼ f ðt ev ; t gc;out Þ
discharge pressure contours and maximum system COP contours are shown in Figs. 5 and 6, respectively, where the evaporator temperature varies from 45 to 5 1C and the gas cooler exit temperature varies from 30 to 60 1C. It may be noted that optimum discharge pressure varies from 73 to 180 bar, whereas the maximum system COP varies from 2.2 to 11.2 and the variations are very similar to the basic valve expansion cycle [10]. Variation clearly shows that the effect of gas cooler exit temperature are much more significant compared with the evaporator temperature on the optimum discharge pressure where as equally significant on maximum system COP. Both the iso-optimum pressure lines and iso-maximum system COP lines are nearly parallel and the optimum pressure vary least towards the minimum gas cooler exit temperature and maximum evaporator temperature, whereas the maximum system COP varies least towards the maximum gas cooler exit temperature and minimum evaporator temperature. So the design of system for lowest possible gas cooler exit temperature and the highest
(17)
Similarly, for MEETC, optimum Pcd and PLR, and maximum COPs can be expressed by P cd;opt ; COP s;max ; PLRopt ¼ f ðt ev ; t gc;out ; mÞ
(18)
4. Results and discussion The present numerical model is verified with the theoretical and experimental data available in open literature [8,14,15]. Performance comparison of CEETC for tev ¼ 2 1C with 5 K superheat, tgc,out ¼ 35 1C, Zn ¼ 0.8, Zd ¼ 0.75 and Zc ¼ 0.8 shows that the optimum discharge pressure (85 bar), entrainment ratio (0.542) and cooling COP (3.68) values are closely matching with design data of experimental prototype, which was validated with test results [14]. Comparison with another experimental results [15] shows similar behavioral trends of entrainment ratio (increases) and pressure lift ratio (decreases) with gas cooler exit pressure, although absolute values comparison is not possible due to insufficient available data. Performance comparison of MEETC for tev ¼ 5 1C with 5 K superheat, tgc,out ¼ 40 1C, Zn ¼ 0.9, Zd ¼ 0.8 and Zc ¼ 0.75 shows also very close result (ratio of COP with ejector and expansion valve is 1.147) with literature data [8]. The performance of both CEETC and MEETC being studied for simultaneous cooling and heating applications are evaluated on the basis of maximum system COP for various evaporator temperature (45 to 5 1C) and gas cooler outlet temperature (30–60 1C). To investigate the characteristics of the ejectorexpansion transcritical CO2 cycle, the pressure drop of secondary flow in the ejector nozzle (P8P9) has been taken as 0.3 bar. The ejector is assumed to have the following efficiencies: Zn ¼ 0.8, Zd ¼ 0.8. The compressor is assumed to have an isentropic efficiency of 0.75. The maximum system COP along with corresponding optimum gas cooler pressure, entrainment ratio and pressure lift ratio are suitably plotted to illustrate the various performance trends.
Fig. 5. Optimum compressor discharge pressure (in bar) contour for CEETC.
4.1. Optimization of conventional ejector-expansion transcritical CO2 cycle The performance of CEETC being studied based on maximum system COP at optimum discharge pressure and corresponding entrainment ratio and pressure lift ratio. Optimum compressor
Fig. 6. Maximum system COP contour for CEETC.
ARTICLE IN PRESS J. Sarkar / Energy 33 (2008) 1399–1406
possible evaporator temperature is more effective for not only maximum system COP also for lower optimum high side pressure. On the other hand, for high-temperature heating application or low-temperature cooling, the system is not profitable in term of system COP as well as cost due to high optimum discharge pressure. The variations of entrainment ratio and pressure lift ratio at optimum discharge pressure with gas cooler exit temperature for different evaporator pressure are shown in Fig. 7. It may be noted that optimum entrainment ratio varies from 0.35 to 0.62, whereas the optimum PLR varies from 1.1 to 1.7 for the given ranges of evaporator and gas cooler exit temperatures. Variations show that the optimum entrainment ratio increases towards the minimum gas cooler exit temperature and maximum evaporator temperature, whereas the optimum PLR increases towards the maximum gas cooler exit temperature and minimum evaporator temperature. As the gas cooler exit temperature increases or the evaporator temperature decreases and corresponding optimum gas cooler pressure increases, the vapor quality is increases at ejector nozzle exit as well as at the diffuser exit of ejector, which gives the lower entrainment ratio. Due to simultaneous increase in nozzle pressure drop with higher optimum gas cooler pressure and decrease in optimum entrainment ratio, kinetic energy increases at the nozzle exit, which can give higher pressure lift in proceeding mixing and diffuser sections and hence the PLR is increases with the increase of gas cooler exit temperature and decrease of evaporator temperature. Performing a regression analysis on the data obtained from the cycle simulation, the following relations have been established to predict estimates the optimum design parameters: optimum discharge pressure in bar (R2 ¼ 99.9%), maximum system COP (R2 ¼ 96.8%), optimum entrainment ratio (R2 ¼ 99.8%) and pres-
0.63
5°C
5°C
5°C
−15°C
15°C
−25°C
−25°C
−35°C
−35°C
−45°C
−45°C
sure lift ratio (R2 ¼ 99.9%), valid for the ranges of the evaporator temperature from 45 to 5 1C and the gas cooler exit temperature from 30 to 60 1C: Pcd;opt ¼ 22:7 þ 0:21t ev þ 1:06t gc;out 0:0094t ev t gc;out þ 0:0213t 2gc;out
(19)
COP s;max ¼ 19:168 þ 0:2662t ev 0:4445t gc;out 0:003458t ev t gc;out þ 0:003007t 2gc;out þ 001086t 2ev (20) mopt ¼ 0:8736 þ 0:00426t ev 0:01086t gc;out 0:00005t ev t gc;out þ 0:000053t 2gc;out
(21)
PLRopt ¼ 0:998 þ 0:0013t ev þ 0:00245t gc;out 0:000107t ev t gc;out þ 0:0000247t 2gc;out þ 000105t 2ev
(22)
4.2. Optimization of modified ejector-expansion transcritical CO2 cycle The optimum performance of MEETC is dependent on evaporator and gas cooler exit temperatures as well as entrainment ratio. Optimum compressor discharge pressure contours and maximum system COP contours for m ¼ 0.6 are shown in Figs. 8 and 9, respectively, for given ranges of evaporator and gas cooler exit temperatures. It may be noted that the variations trends are similar as for CEETC, although the optimum discharge pressure gives higher value, varies from 74 to 195 bar and the maximum system COP gives lower value, varies from 2.1 to 10. Void portion in both contour plots indicates that the optimization of MEETC cannot be realized at that lower gas cooler exit temperature and higher evaporator temperature. Similar to CEETC, the effect of gas cooler exit temperature is much more significant compared with the evaporator temperature on the optimum discharge pressure whereas equally significant on maximum system COP. Results indicate that the design of system for lowest possible gas cooler exit temperature and the highest possible evaporator temperature
1.7
µ - without marker PLR - with marker
0.59
1.6
0.55
1.5
0.51
1.4
0.47
1.3
0.43
1.2
0.39
1.1
0.35
Pressure lift ratio
Entrainment ratio
5°C
1403
1 30
40 35 45 50 55 Gas cooler outlet temperature (°C)
60
Fig. 7. Variation of optimum m and PLR with gas cooler outlet temperature for different evaporation temperatures.
Fig. 8. Optimum discharge pressure (bar) contour for MEETC at m ¼ 0.6.
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5°C
5°C
15°C
15°C
−30°C
30°C
−45°C
45°C 0.2
1.44 PLR -with marker 1.38
Pressure lift ratio
1.32 0.12 1.26 0.08 1.2
Feed back vapor fraction
0.16
0.04
1.14 Fig. 9. Maximum system COP contour for MEETC at m ¼ 0.6.
0
1.08
P cd;opt ¼ 19:96 þ 0:356t ev þ 0:965t gc;out 0:01535t ev t gc;out þ 02485t 2gc;out þ 3:9m
0:002812t ev t gc;out þ 0:002246t 2gc;out (24)
PLRopt ¼ 1:2 0:0044t ev þ 0:0043t gc;out 0:000021t ev t gc;out 0:000015t 2gc;out 0:385m
40 45 50 55 Gas cooler outlet temperature (°C)
60
2.9 6.5 2.8
te = −45°C, tco = 40°C te = −45°C, tco = 50°C
2.6
te = 5°C, tco = 40°C
5.5
te = 5°C, tco = 50°C
System COP
6 2.7
2.5 5 2.4 2.3 0.5
0.55
0.6 Entrainment ratio
0.65
4.5 0.7
Fig. 11. System COP variation with entrainment ratio at optimum condition.
4.3. Energetic comparison of different expansion device-based CO2 cycles
(23)
COP s;max ¼ 17:33 þ 0:1913t ev 0:3628t gc;out 0:707m
35
Fig. 10. Variation of PLR and feedback fraction at optimum discharge pressure with gas cooler outlet temperature for different evaporation temperature for m ¼ 0.6.
System COP
is profitable in term of system COP as well as cost due to lower optimum discharge pressure. The variations of PLR and feedback vapor fraction ( ¼ 1[x5(1+m)]1) at optimum discharge pressure with gas cooler exit temperature for different evaporator pressure are shown in Fig. 10. With the increase in gas cooler exit temperature and decrease in evaporator temperature, nozzle pressure drop increases as increase in optimum gas cooler pressure, which gives higher PLR due to same reason discussed before. As the optimum gas cooler pressure increases with the increase in gas cooler exit temperature or decrease in evaporator temperature, the vapour quality increases at ejector nozzle exit as well as at the diffuser exit of ejector, which gives the higher feedback fraction. Effect of entrainment ratio on optimum discharge pressure is negligible, whereas the system COP decreases with increase in entrainment ratio moderately as shown in Fig. 11. PLR decreases due to decrease in kinetic energy at mixing section exit with the increase in entrainment ratio. Optimum correlations for CEETC are significant in such a way that the MEETC can be realised either above the mopt (in Eq. (21)) for fixed discharge pressure at Pcd,opt (in Eq. (19)) or bellow Pcd,opt for fixed entrainment ratio at mopt Performing a regression analysis, the following relations for MEETC have been established to predict optimum discharge pressure in bar (R2 ¼ 99.9%), maximum system COP (R2 ¼ 97%) and pressure lift ratio (R2 ¼ 97.5%), valid for the ranges of the evaporator temperature from 45 to 5 1C, gas cooler exit temperature from 32 to 60 1C and entrainment ratio from 0.52 to 0.6:
30
(25)
A comparison of CEETC and MEETC (m ¼ 0.6) with basic valve expansion transcritical CO2 cycle (VETC) and turbine expansion transcritical CO2 cycle (TETC) in terms of optimum discharge pressure and maximum system COP with gas cooler exit temperature for the turbine isentropic efficiency of 80% are shown in Figs. 12 and 13 at the evaporator temperatures of 5 and 451C, respectively. The difference between valve and turbine expansion cycles is related to expansion process [16]: for valve, expansion process is isenthalpic and system COP is calculated as
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12.2 VETC TETC CEETC MEETC
157 145
Table 1 Exergetic comparison of different expansion device-based CO2 cycles, tco ¼ 40 1C
11.2 10.2 9.2
133 8.2 121 7.2 109
6.2
97
Maximum system COP
Optimum discharge pressure (bar)
169
5.2
85
4.2
tev = 5°C
3.2
73 30
35 40 45 50 55 Gas cooler exit temperature (°C)
60
Fig. 12. Comparison of difference cycles with gas cooler exit temperature, tev ¼ 5 1C.
4
208 VETC TETC CEETC MEETC
178
3.7 3.4
163 148
3.1
133
2.8
118 2.5
Maximum system COP
Optimum discharge pressure (bar)
193
103 2.2
88
tev = –45°C
73
1405
Cycle
VETC
tev (1C) tso (1C) ZII (%) ied (%)
5 64.3 35.99 30.80
TETC 45 114.1 42.84 29.54
5 59.0 44.52 9.07
CEETC 45 89.5 53.30 8.54
5 59.7 37.16 27.18
MEETC 45 92.7 45.68 24.94
5 61.06 37.21 28.00
45 102.6 46.04 26.58
simultaneous constant temperature cooling at Tev+TA and variable temperature heating from Tsi to Tso. The second law efficiency is calculated by To ZII ¼ qev 1 T ev þ TA T o lnðT so =T si Þ (26) wnet þ qgc 1 T so T si where wnet is difference between compressor and turbine works for TETC, otherwise wnet ¼ wc and temperatures are in K; To ¼ Tsi ¼ 303.15 K and TA ¼ 5 K. Tso is found by iteration technique to satisfy TA at pinch point. Percentages of expansion exergy loss of VETC, TETC have been calculated based on entropy change of expansion device [9,16] and for CEETC and MEETC, same have been calculated based on combined exergy losses for expansion valve and ejector, which are given by, respectively: 1 m m s3 s8 þ ðs7 s6 Þ ied ¼ T o s5 wc (27) 1þm 1þm 1þm 1 m s3 s8 þ ð1 x5 Þðs7 s6 Þ s5 1þm 1þm 1 ðs11 s1 Þ þ x5 wc 1þm
ied ¼ T o
(28)
Results indicated that the expansion exergy loss of ejector is lower that of valve and second law efficiency of transcritical CO2 system can also improve by using ejector over the valve (maximum improvement of 9% can be obtain over the studied ranges). Exergetic performance of TETC is significantly better than that of other cycles with penalty of higher cost associated with turbine.
1.9 30
35
40
45
50
55
60
Gas cooler exit temperature (°C) Fig. 13. Comparison of difference cycles with gas cooler exit temperature, tev ¼ 45 1C.
combined output by compressor work, whereas, for turbine, expansion process is near isentropic and system COP is calculated as combined output by net work (compressor work–turbine work). It can be noted that the performance difference between CEETC and MEETC are negligible at higher evaporator temperature due to values of m closer to 0.6. Results clearly shows that the both CEETC and TETC are better in terms of optimum discharge pressure as well as system COP. Although TETC is better with respect to both low cost associated with lower optimum discharge pressure and higher maximum system COP, negligible cost associated with ejector as compared with turbine can make the ejector-driven cycles more profitable for the low capacity heat pump applications. 4.4. Exergetic comparison of different expansion device-based CO2 cycles Second law-based compression of VETC, TETC, CEETC and MEETC at optimum discharge pressure are listed in Table 1 for
5. Conclusions Optimizations of ejector-expansion transcritical CO2 heat pump cycle for simultaneous cooling and heating with conventional layout as well as modified layout, followed by energetic and exergetic comparison with valve and turbine expansion cycles are presented here. Studies shows that the effect of gas cooler outlet temperature is more predominant compared with evaporator temperature on both CEETC and MEETC performances. Optimum entrainment ratio increases towards the minimum gas cooler exit temperature and maximum evaporator temperature, whereas the optimum PLR increases towards the maximum gas cooler exit temperature and minimum evaporator temperature for CEETC. Effect of entrainment ratio on discharge pressure is negligible compared with COP at optimum conditions for MEETC. The MEETC can be realized for certain discharge pressure and entrainment ratio combinations. CEETC is always better than MEETC in term of system COP as well as cost due to lower optimum discharge pressure. Expressions for optimum cycle parameters for both CEETC and MEETC have been developed and these correlations offer useful guidelines for optimal system design and for selecting appropriated operating conditions. Both energetic and exergetic performance wise, CEETC and MEETC are better compared with
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VETC, but poorer compared with TETC. Second law efficiency can be improved by maximum 9% by using ejector over valve for given ranges. In view of the trade-off between the system performance and cost associated with expansion devices, the ejector may be the best alternative expansion device at least for low-capacity transcritical CO2 heat pump systems. References [1] Groll EA. Recent advances in the transcritical CO2 cycle technology. In: Eighth national and seventh ISHMT-ASME heat and mass transfer conference, IIT Guahati, India, 2006. [2] Hrnjak PS. Improvement options for CO2 and R134a systems, MAC Summit, Saalfelden, Austria, 2006. [3] Groll EA, Kim JH. Review of recent advances toward transcritical CO2 cycle technology. HVAC&R Research 2007;13(3):499–520. [4] Kornhauser AA. The use of an ejector as a refrigerant expander. In: Proceedings of the 1990 USNC/IIR-Purdue refrigeration conference, USA, 1990. p. 10–9. [5] Liu JP, Chen JP, Chen ZJ. Thermodynamic analysis on trans-critical R744 vaporcompression/ejection hybrid refrigeration cycle. In: Proceedings of the fifth IIR Gustav Lorentzen conference on natural working fluids, Guangzhou, China, 2002. p. 184–8. [6] Elbel SW, Hrnjak PS. Effect of internal heat exchanger on performance of transcritical CO2 systems with ejector. In: Proceedings of the 10th interna-
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[16]
tional refrigeration and air conditioning conference, Purdue, West Lafayette, IN, USA, 2004. Ozaki Y, Takeuchi H, Hirata T. Regeneration of expansion energy by ejector in CO2 cycle. In: Sixth IIR Gustav Lorentzen natural working fluid conference, Glasgow, UK, 2004. Paper 4/A/11.20. Li D, Groll EA. Transcritical CO2 refrigeration cycle with ejector-expansion device. Int J Refrig 2005;28(5):766–73. Deng J, Jiang P, Lu T, Lu W. Particular characteristics of transcritical CO2 refrigeration cycle with an ejector. Appl Therm Eng 2007;27: 381–8. Sarkar J, Bhattacharyya S, Ramgopal M. Optimization of a transcritical CO2 heat pump cycle for simultaneous cooling and heating applications. Int J Refrig 2004;27(8):830–8. Chen Y, Gu J. The optimum high pressure for CO2 transcritical refrigeration systems with internal heat exchangers. Int J Refrig 2005;28:1238–49. Agrawal N, Bhattacharyya S, Sarkar J. Optimization of two-stage transcritical carbon dioxide heat pump cycles. Int J Thermal Sci 2007;46(2):180–7. Chunnanond K, Aphornratana S. Ejectors: applications in refrigeration technology. Renew Sust Energy Rev 2004;8:129–55. Ksayer EB, Clodic D. CO2 ejector refrigeration cycle: design, tests and results. In: Twenty-second international congress of refrigeration, Beijing, 2007. Paper 1590. Elbel S, Hrnjak P. Experimental investigation of transcritical CO2 ejector system performance. In: Twenty-second international congress of refrigeration, Beijing, 2007. Paper 72. Robinson DM, Groll EA. Efficiencies of transcritical CO2 cycles with and without an expansion turbine. Int J Refrig 1998;21(7):577–89.
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Optimization of ejector-expansion transcritical CO2 heat pump cycle Jahar Sarkar Department of Mechanical Engineering, Institute of Technology, BHU, Varanasi 221005, India
a r t i c l e in fo
abstract
Article history: Received 28 December 2007
Optimization studies along with optimum parameter correlations, using constant area mixing model are presented in this article for ejector-expansion transcritical CO2 heat pump cycle with both conventional and modified layouts. Both the energetic and exergetic comparisons between valve, turbine and ejector-expansions-based transcritical CO2 heat pump cycles are also studied for simultaneous cooling and heating applications. Performances for conventional layouts are presented by maximum COP, optimum discharge pressure and corresponding entrainment ratio and pressure lift ratio of ejector, whereas for modified layout by maximum COP, optimum discharge pressure and corresponding pressure lift ratio. The optimization for modified layout can be realized for certain entrainment ratio, evaporator and gas cooler exit temperature combinations. Considering the trade-off between the system energetic and exergetic performances, and cost associated with expansion devices, the ejector may be the promising alternative expansion device for transcritical CO2 heat pump cycle. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Ejector-expansion CO2 cycle Modelling Entrainment ratio Pressure lift ratio Optimization Performance comparison
1. Introduction Use of ejector as an expansion device in transcritical CO2 cycle seems to be a promising modification to improve the system performance [1–3]. Kornhauser [4] analyzed the thermodynamic performance of the ejector-expansion refrigeration cycle using R12 as a refrigerant based on constant mixing pressure model and found a COP improvement of up to 21% over the standard cycle under standard operating conditions. Liu et al. [5] first performed a thermodynamic analysis of the transcritical CO2 vapor compression/ejection hybrid refrigeration cycle. Another theoretical study on transcritical CO2 systems with ejector to study the effect of internal heat exchanger on the performance was reported by Elbel et al. [6]. Use of ejector in transcritical CO2 cycle not only improve the COP, also simplifies the process of controlling the gas cooler pressure in the CO2 cycle by changing the throat area of the ejector nozzle [7]. Experiment showed that the COP of the car airconditioner using the ejector cycle increases by 20% over the conventional cycle [7]. Ejector is much more beneficial to CO2 systems with maximum COP improvement of 44% compared with R134a system of 13% for 100% isentropic ejector efficiency, however, key is to build highly efficient ejectors [2]. Li and Groll [8] recently modified the ejector-expansion cycle by allowing part of the vapor in the separator feed back to the evaporator, which regulates the quality at the evaporator inlet and through theoretical analysis, they showed the COP improvement
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to be more than 16%. Through comparative study, Deng et al. [9] showed that the ejector improves the maximum COP by up to 18.6% compared with the internal heat exchanger system and by 22.0% compared with the conventional system with greatly reducing the throttling losses. Although optimization studies for other cycle modifications have been reported in open literature [10–12], such theoretical optimization studies with ejector for simultaneous cooling and heating are scarce. The present study, on transcritical CO2 cycle for simultaneous cooling and heating, consists of three parts. The first part presents the optimization of high pressure along with entrainment ratio and pressure lift ratio based on the maximum system COP for the ejector-expansion transcritical CO2 heat pump cycle with conventional layout (CEETC) by using constant area mixing model. The second part presents the optimization of ejector-expansion transcritical CO2 heat pump cycle with modified layout (MEETC) by using constant area mixing model. The third part presents the comparison of optimum high side pressure, performances and expansion exergy loss for transcritical CO2 heat pump cycle based on three expansion devices: valve, turbine and ejector.
2. Ejector-expansion CO2 heat pump cycle layout In the present study, the compressor discharge pressure optimization to get the maximum COP has been done for two ejector-driven transcritical CO2 cycle layouts. First one is the conventional ejector-driven cycle, proposed by Kornhauser [4], which is shown in Fig. 1 and the corresponding P–h diagram is shown in Fig. 2. The primary flow from the gas cooler and the
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Nomenclature a TA COPs h P PLR q t,T T0 u w x m r Z
ZII
cross-sectional area (m2) temperature approach (K) system coefficient of performance specific enthalpy (kJ/kg) pressure (bar) pressure lift ratio specific cooling/heating effect (kJ/kg) temperature (1C, K) reference temperature (K) fluid velocity (m/s) specific work (kJ/kg) vapor quality entrainment ratio fluid density (kg/m3) isentropic efficiency
second law efficiency
Subscripts c cd d ed ej ev gc gc,out max n opt si/so
compressor compressor discharge ejector diffuser expansion device ejector evaporator gas cooler gas cooler outlet maximum ejector nozzle optimum secondary fluid inlet/outlet
secondary flow from the evaporator are passing through nozzle, mixing and diffuser sections of the ejector and then separating in forms of vapor and liquid so that this ratio should matched with the inlet ratio of primary and secondary flows. Second one is the modified ejector-driven cycle, proposed by Li and Groll [8], which is shown in Fig. 3 and the corresponding P–h diagram is shown in Fig. 4. The main difference with conventional ejector cycle is that some part of vapor from separator is feed back to evaporator through throttle valve to regulate the quality of evaporator inlet. Two ejector performance parameters significantly influence the system performance with an optimum ratio, which can be defined by [13] Entrainment ratio; m ¼
masss of secondary flow mass of primary flow
Pressure lift ratio; PLR ¼
(1)
static pressure at diffuser exit static pressure at secondary flow inlet (2)
Fig. 1. Schematic diagram of conventional ejector-expansion transcritical CO2 cycle.
3. Mathematical modeling and simulation The ejector-driven transcritical CO2 heat pump cycle for the both layouts has been modeled based on the mass, momentum and the energy conservations. To simplify the theoretical model and set up the equations per unit total ejector flow for the both cycle layouts, the following assumptions are made:
Pgc
2
Pressure
3
5
6
1 8
7 4
10
Pev
9
Specific enthalpy Fig. 2. P–h diagram of conventional ejector-expansion transcritical CO2 cycle.
(i) Neglect the pressure drop in the gas cooler and evaporator and the connection tubes. (ii) No heat transfer with the environment for the system. (iii) The refrigerant condition at the evaporator outlet is saturated. (iv) The vapor stream from the separator is saturated vapor and the liquid stream from the separator is saturated liquid. (v) The flow across the expansion valve or the throttle valves is isenthalpic. (vi) The compressor has a given isentropic efficiency. (vii) Both the motive stream and the suction stream reach the same pressure at the inlet of the constant area mixing section of the ejector. There is no mixing between the two streams before the inlet of the constant area mixing section. (viii) The expansion efficiencies of the motive stream and suction stream are given constants. The diffuser of the ejector also has a given efficiency.
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1401
And for the diffuser section the energy balance is given by h5 ¼ h10 þ u210 =2
(8)
The overall energy balance in the ejector for both cycle layouts is given by ð1 þ mÞh5 ¼ h3 þ mh8
(9)
For both cycle layouts, the specific compressor work and heating effect can be found by wc ¼
1 ðh2 h1 Þ 1þm
(10)
qgc ¼
1 ðh2 h3 Þ 1þm
(11)
For the conventional ejector cycle (Fig. 1), the specific cooling effect: Fig. 3. Schematic diagram of modified CO2 cycle with ejector-expansion device.
qev ¼
m ðh8 h6 Þ 1þm
Whereas for the modified ejector cycle (Fig. 3), m 1 h8 ð1 x5 Þh6 x5 h1 qev ¼ 1þm 1þm
Pgc
3
2
Pressure
1 8
7 4
10
Pev
9
0 Specific enthalpy Fig. 4. P–h diagram of modified ejector-expansion transcritical CO2 cycle.
(ix) Kinetic energies of the refrigerant at the ejector inlet and outlet are negligible. Based on the above assumptions, the following equations can be setup in the nozzle section of ejector for both the layouts: h3 ¼ h4 þ u24 =2
(3)
h8 ¼ h9 þ u29 =2
(4)
For given entrainment ratio, the following mass, momentum and energy equations in the constant area mixing section of ejector can be identified for both cycle layouts [8]: (5)
u10 ¼ ðu4 þ mu9 Þ=ð1 þ mÞ P 10 ða4 þ a9 Þ þ u10 ¼ P9 ða4 þ a9 Þ þ
h10 þ
2
u210 u 1 h4 þ 4 ¼ 1þm 2 2
1 m u4 þ u9 1þm 1þm
u2 m h9 þ 9 þ 1þm 2
(14)
Based on the theoretical model of ejector-driven transcritical CO2 heat pump cycles, the simulation code was developed to investigate the effect of different operating parameters for both layouts, which was integrated with the thermodynamic property code CO2PROP [10] to compute relevant thermodynamic parameters of carbon dioxide in sub- and super-critical regions. For given compressor discharge pressure, evaporator and gas cooler exit temperatures, the algorithm of code for conventional cycle is as follows:
5 11
(13)
The system COP (combined cooling and heating) can be calculated by COP s ¼ ðqev þ qgc Þ=wc
6
(12)
(6)
(7)
(i) Properties at states 8 and 3 are calculated. Enthalpies and other thermodynamic properties at states 9 and 4 are calculated by given nozzle efficiency and P8–P9. Velocities at the corresponding states are calculated by using Eqs. (3) and (4) and then areas are also calculated. (ii) Some value of entrainment ratio is assumed for iteration. (iii) Using Eqs. (5)–(7), the pressure, enthalpy and fluid velocity at exit of mixing section (state 10) are calculated by effective iteration technique, which satisfy the condition: r10(a4+a9)u10 ¼ 1 (for unit flow rate) and then other properties are calculated. (iv) Using Eqs. (9) or (8) and given diffuser efficiency, enthalpy, pressure and vapor quality at state 5 are calculated and then other properties are also calculated. (v) If the condition (1+m)x5 ¼ 1 is not satisfied, steps (iii)–(iv) will repeated by using new value of m [ ¼ (1x5)/x5] until the condition satisfied. (vi) Properties at states 6, 7 and 1 are calculated. Then the properties of state 2 are calculated using given compressor isentropic efficiency. (vii) Using Eqs. (10)–(12) and (14), the performance parameters: wc, qev, qgc and COPs are calculated and PLR ( ¼ P1/Pev) is also calculated. For the modified ejector-driven cycle simulation, similar algorithm has been used excluding iteration loop for entrainment ratio as it is user defined, i.e. steps (i), (iii)–(iv), (vi)–(vii), only qev is calculated by using Eq. (13) instead of Eq. (12) at the last step.
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In the present numerical model, following tolerances have been used for convergence in simulation for the overall satisfaction: 103 for temperature (K) and enthalpy (kJ/kg), 104 for mass flow rate (0.01% for unit mass flow rate) and 105 for entrainment ratio, which may give the error for mass balance as 0.01%, in energy balance below 0.01% and system COP computation in the range of 104. The ejector-driven transcritical CO2 cycle for combined cooling and heating applications is optimized on the basis of maximum system COP. These values are obtained for various operating conditions along with variation of the compressor discharge pressure having a step size of 0.5 bar. In general, for the CEETC and MEETC, respectively, the system COP can be expressed by COP sys ¼ f ðt ev ; t gc;out ; P 8 P 9 ; P d ; Zc ; Zn ; Zd Þ
(15)
COP sys ¼ f ðt ev ; t gc;out ; P 8 P 9 ; P d ; m; Zc ; Zn ; Zd Þ
(16)
Based on the assumptions made, the optimum discharge pressure, entrainment ratio and pressure lift ratio and maximum system COP for CEETC are expressed by P cd;opt ; COP s;max ; mopt ; PLRopt ¼ f ðt ev ; t gc;out Þ
discharge pressure contours and maximum system COP contours are shown in Figs. 5 and 6, respectively, where the evaporator temperature varies from 45 to 5 1C and the gas cooler exit temperature varies from 30 to 60 1C. It may be noted that optimum discharge pressure varies from 73 to 180 bar, whereas the maximum system COP varies from 2.2 to 11.2 and the variations are very similar to the basic valve expansion cycle [10]. Variation clearly shows that the effect of gas cooler exit temperature are much more significant compared with the evaporator temperature on the optimum discharge pressure where as equally significant on maximum system COP. Both the iso-optimum pressure lines and iso-maximum system COP lines are nearly parallel and the optimum pressure vary least towards the minimum gas cooler exit temperature and maximum evaporator temperature, whereas the maximum system COP varies least towards the maximum gas cooler exit temperature and minimum evaporator temperature. So the design of system for lowest possible gas cooler exit temperature and the highest
(17)
Similarly, for MEETC, optimum Pcd and PLR, and maximum COPs can be expressed by P cd;opt ; COP s;max ; PLRopt ¼ f ðt ev ; t gc;out ; mÞ
(18)
4. Results and discussion The present numerical model is verified with the theoretical and experimental data available in open literature [8,14,15]. Performance comparison of CEETC for tev ¼ 2 1C with 5 K superheat, tgc,out ¼ 35 1C, Zn ¼ 0.8, Zd ¼ 0.75 and Zc ¼ 0.8 shows that the optimum discharge pressure (85 bar), entrainment ratio (0.542) and cooling COP (3.68) values are closely matching with design data of experimental prototype, which was validated with test results [14]. Comparison with another experimental results [15] shows similar behavioral trends of entrainment ratio (increases) and pressure lift ratio (decreases) with gas cooler exit pressure, although absolute values comparison is not possible due to insufficient available data. Performance comparison of MEETC for tev ¼ 5 1C with 5 K superheat, tgc,out ¼ 40 1C, Zn ¼ 0.9, Zd ¼ 0.8 and Zc ¼ 0.75 shows also very close result (ratio of COP with ejector and expansion valve is 1.147) with literature data [8]. The performance of both CEETC and MEETC being studied for simultaneous cooling and heating applications are evaluated on the basis of maximum system COP for various evaporator temperature (45 to 5 1C) and gas cooler outlet temperature (30–60 1C). To investigate the characteristics of the ejectorexpansion transcritical CO2 cycle, the pressure drop of secondary flow in the ejector nozzle (P8P9) has been taken as 0.3 bar. The ejector is assumed to have the following efficiencies: Zn ¼ 0.8, Zd ¼ 0.8. The compressor is assumed to have an isentropic efficiency of 0.75. The maximum system COP along with corresponding optimum gas cooler pressure, entrainment ratio and pressure lift ratio are suitably plotted to illustrate the various performance trends.
Fig. 5. Optimum compressor discharge pressure (in bar) contour for CEETC.
4.1. Optimization of conventional ejector-expansion transcritical CO2 cycle The performance of CEETC being studied based on maximum system COP at optimum discharge pressure and corresponding entrainment ratio and pressure lift ratio. Optimum compressor
Fig. 6. Maximum system COP contour for CEETC.
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possible evaporator temperature is more effective for not only maximum system COP also for lower optimum high side pressure. On the other hand, for high-temperature heating application or low-temperature cooling, the system is not profitable in term of system COP as well as cost due to high optimum discharge pressure. The variations of entrainment ratio and pressure lift ratio at optimum discharge pressure with gas cooler exit temperature for different evaporator pressure are shown in Fig. 7. It may be noted that optimum entrainment ratio varies from 0.35 to 0.62, whereas the optimum PLR varies from 1.1 to 1.7 for the given ranges of evaporator and gas cooler exit temperatures. Variations show that the optimum entrainment ratio increases towards the minimum gas cooler exit temperature and maximum evaporator temperature, whereas the optimum PLR increases towards the maximum gas cooler exit temperature and minimum evaporator temperature. As the gas cooler exit temperature increases or the evaporator temperature decreases and corresponding optimum gas cooler pressure increases, the vapor quality is increases at ejector nozzle exit as well as at the diffuser exit of ejector, which gives the lower entrainment ratio. Due to simultaneous increase in nozzle pressure drop with higher optimum gas cooler pressure and decrease in optimum entrainment ratio, kinetic energy increases at the nozzle exit, which can give higher pressure lift in proceeding mixing and diffuser sections and hence the PLR is increases with the increase of gas cooler exit temperature and decrease of evaporator temperature. Performing a regression analysis on the data obtained from the cycle simulation, the following relations have been established to predict estimates the optimum design parameters: optimum discharge pressure in bar (R2 ¼ 99.9%), maximum system COP (R2 ¼ 96.8%), optimum entrainment ratio (R2 ¼ 99.8%) and pres-
0.63
5°C
5°C
5°C
−15°C
15°C
−25°C
−25°C
−35°C
−35°C
−45°C
−45°C
sure lift ratio (R2 ¼ 99.9%), valid for the ranges of the evaporator temperature from 45 to 5 1C and the gas cooler exit temperature from 30 to 60 1C: Pcd;opt ¼ 22:7 þ 0:21t ev þ 1:06t gc;out 0:0094t ev t gc;out þ 0:0213t 2gc;out
(19)
COP s;max ¼ 19:168 þ 0:2662t ev 0:4445t gc;out 0:003458t ev t gc;out þ 0:003007t 2gc;out þ 001086t 2ev (20) mopt ¼ 0:8736 þ 0:00426t ev 0:01086t gc;out 0:00005t ev t gc;out þ 0:000053t 2gc;out
(21)
PLRopt ¼ 0:998 þ 0:0013t ev þ 0:00245t gc;out 0:000107t ev t gc;out þ 0:0000247t 2gc;out þ 000105t 2ev
(22)
4.2. Optimization of modified ejector-expansion transcritical CO2 cycle The optimum performance of MEETC is dependent on evaporator and gas cooler exit temperatures as well as entrainment ratio. Optimum compressor discharge pressure contours and maximum system COP contours for m ¼ 0.6 are shown in Figs. 8 and 9, respectively, for given ranges of evaporator and gas cooler exit temperatures. It may be noted that the variations trends are similar as for CEETC, although the optimum discharge pressure gives higher value, varies from 74 to 195 bar and the maximum system COP gives lower value, varies from 2.1 to 10. Void portion in both contour plots indicates that the optimization of MEETC cannot be realized at that lower gas cooler exit temperature and higher evaporator temperature. Similar to CEETC, the effect of gas cooler exit temperature is much more significant compared with the evaporator temperature on the optimum discharge pressure whereas equally significant on maximum system COP. Results indicate that the design of system for lowest possible gas cooler exit temperature and the highest possible evaporator temperature
1.7
µ - without marker PLR - with marker
0.59
1.6
0.55
1.5
0.51
1.4
0.47
1.3
0.43
1.2
0.39
1.1
0.35
Pressure lift ratio
Entrainment ratio
5°C
1403
1 30
40 35 45 50 55 Gas cooler outlet temperature (°C)
60
Fig. 7. Variation of optimum m and PLR with gas cooler outlet temperature for different evaporation temperatures.
Fig. 8. Optimum discharge pressure (bar) contour for MEETC at m ¼ 0.6.
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5°C
5°C
15°C
15°C
−30°C
30°C
−45°C
45°C 0.2
1.44 PLR -with marker 1.38
Pressure lift ratio
1.32 0.12 1.26 0.08 1.2
Feed back vapor fraction
0.16
0.04
1.14 Fig. 9. Maximum system COP contour for MEETC at m ¼ 0.6.
0
1.08
P cd;opt ¼ 19:96 þ 0:356t ev þ 0:965t gc;out 0:01535t ev t gc;out þ 02485t 2gc;out þ 3:9m
0:002812t ev t gc;out þ 0:002246t 2gc;out (24)
PLRopt ¼ 1:2 0:0044t ev þ 0:0043t gc;out 0:000021t ev t gc;out 0:000015t 2gc;out 0:385m
40 45 50 55 Gas cooler outlet temperature (°C)
60
2.9 6.5 2.8
te = −45°C, tco = 40°C te = −45°C, tco = 50°C
2.6
te = 5°C, tco = 40°C
5.5
te = 5°C, tco = 50°C
System COP
6 2.7
2.5 5 2.4 2.3 0.5
0.55
0.6 Entrainment ratio
0.65
4.5 0.7
Fig. 11. System COP variation with entrainment ratio at optimum condition.
4.3. Energetic comparison of different expansion device-based CO2 cycles
(23)
COP s;max ¼ 17:33 þ 0:1913t ev 0:3628t gc;out 0:707m
35
Fig. 10. Variation of PLR and feedback fraction at optimum discharge pressure with gas cooler outlet temperature for different evaporation temperature for m ¼ 0.6.
System COP
is profitable in term of system COP as well as cost due to lower optimum discharge pressure. The variations of PLR and feedback vapor fraction ( ¼ 1[x5(1+m)]1) at optimum discharge pressure with gas cooler exit temperature for different evaporator pressure are shown in Fig. 10. With the increase in gas cooler exit temperature and decrease in evaporator temperature, nozzle pressure drop increases as increase in optimum gas cooler pressure, which gives higher PLR due to same reason discussed before. As the optimum gas cooler pressure increases with the increase in gas cooler exit temperature or decrease in evaporator temperature, the vapour quality increases at ejector nozzle exit as well as at the diffuser exit of ejector, which gives the higher feedback fraction. Effect of entrainment ratio on optimum discharge pressure is negligible, whereas the system COP decreases with increase in entrainment ratio moderately as shown in Fig. 11. PLR decreases due to decrease in kinetic energy at mixing section exit with the increase in entrainment ratio. Optimum correlations for CEETC are significant in such a way that the MEETC can be realised either above the mopt (in Eq. (21)) for fixed discharge pressure at Pcd,opt (in Eq. (19)) or bellow Pcd,opt for fixed entrainment ratio at mopt Performing a regression analysis, the following relations for MEETC have been established to predict optimum discharge pressure in bar (R2 ¼ 99.9%), maximum system COP (R2 ¼ 97%) and pressure lift ratio (R2 ¼ 97.5%), valid for the ranges of the evaporator temperature from 45 to 5 1C, gas cooler exit temperature from 32 to 60 1C and entrainment ratio from 0.52 to 0.6:
30
(25)
A comparison of CEETC and MEETC (m ¼ 0.6) with basic valve expansion transcritical CO2 cycle (VETC) and turbine expansion transcritical CO2 cycle (TETC) in terms of optimum discharge pressure and maximum system COP with gas cooler exit temperature for the turbine isentropic efficiency of 80% are shown in Figs. 12 and 13 at the evaporator temperatures of 5 and 451C, respectively. The difference between valve and turbine expansion cycles is related to expansion process [16]: for valve, expansion process is isenthalpic and system COP is calculated as
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12.2 VETC TETC CEETC MEETC
157 145
Table 1 Exergetic comparison of different expansion device-based CO2 cycles, tco ¼ 40 1C
11.2 10.2 9.2
133 8.2 121 7.2 109
6.2
97
Maximum system COP
Optimum discharge pressure (bar)
169
5.2
85
4.2
tev = 5°C
3.2
73 30
35 40 45 50 55 Gas cooler exit temperature (°C)
60
Fig. 12. Comparison of difference cycles with gas cooler exit temperature, tev ¼ 5 1C.
4
208 VETC TETC CEETC MEETC
178
3.7 3.4
163 148
3.1
133
2.8
118 2.5
Maximum system COP
Optimum discharge pressure (bar)
193
103 2.2
88
tev = –45°C
73
1405
Cycle
VETC
tev (1C) tso (1C) ZII (%) ied (%)
5 64.3 35.99 30.80
TETC 45 114.1 42.84 29.54
5 59.0 44.52 9.07
CEETC 45 89.5 53.30 8.54
5 59.7 37.16 27.18
MEETC 45 92.7 45.68 24.94
5 61.06 37.21 28.00
45 102.6 46.04 26.58
simultaneous constant temperature cooling at Tev+TA and variable temperature heating from Tsi to Tso. The second law efficiency is calculated by To ZII ¼ qev 1 T ev þ TA T o lnðT so =T si Þ (26) wnet þ qgc 1 T so T si where wnet is difference between compressor and turbine works for TETC, otherwise wnet ¼ wc and temperatures are in K; To ¼ Tsi ¼ 303.15 K and TA ¼ 5 K. Tso is found by iteration technique to satisfy TA at pinch point. Percentages of expansion exergy loss of VETC, TETC have been calculated based on entropy change of expansion device [9,16] and for CEETC and MEETC, same have been calculated based on combined exergy losses for expansion valve and ejector, which are given by, respectively: 1 m m s3 s8 þ ðs7 s6 Þ ied ¼ T o s5 wc (27) 1þm 1þm 1þm 1 m s3 s8 þ ð1 x5 Þðs7 s6 Þ s5 1þm 1þm 1 ðs11 s1 Þ þ x5 wc 1þm
ied ¼ T o
(28)
Results indicated that the expansion exergy loss of ejector is lower that of valve and second law efficiency of transcritical CO2 system can also improve by using ejector over the valve (maximum improvement of 9% can be obtain over the studied ranges). Exergetic performance of TETC is significantly better than that of other cycles with penalty of higher cost associated with turbine.
1.9 30
35
40
45
50
55
60
Gas cooler exit temperature (°C) Fig. 13. Comparison of difference cycles with gas cooler exit temperature, tev ¼ 45 1C.
combined output by compressor work, whereas, for turbine, expansion process is near isentropic and system COP is calculated as combined output by net work (compressor work–turbine work). It can be noted that the performance difference between CEETC and MEETC are negligible at higher evaporator temperature due to values of m closer to 0.6. Results clearly shows that the both CEETC and TETC are better in terms of optimum discharge pressure as well as system COP. Although TETC is better with respect to both low cost associated with lower optimum discharge pressure and higher maximum system COP, negligible cost associated with ejector as compared with turbine can make the ejector-driven cycles more profitable for the low capacity heat pump applications. 4.4. Exergetic comparison of different expansion device-based CO2 cycles Second law-based compression of VETC, TETC, CEETC and MEETC at optimum discharge pressure are listed in Table 1 for
5. Conclusions Optimizations of ejector-expansion transcritical CO2 heat pump cycle for simultaneous cooling and heating with conventional layout as well as modified layout, followed by energetic and exergetic comparison with valve and turbine expansion cycles are presented here. Studies shows that the effect of gas cooler outlet temperature is more predominant compared with evaporator temperature on both CEETC and MEETC performances. Optimum entrainment ratio increases towards the minimum gas cooler exit temperature and maximum evaporator temperature, whereas the optimum PLR increases towards the maximum gas cooler exit temperature and minimum evaporator temperature for CEETC. Effect of entrainment ratio on discharge pressure is negligible compared with COP at optimum conditions for MEETC. The MEETC can be realized for certain discharge pressure and entrainment ratio combinations. CEETC is always better than MEETC in term of system COP as well as cost due to lower optimum discharge pressure. Expressions for optimum cycle parameters for both CEETC and MEETC have been developed and these correlations offer useful guidelines for optimal system design and for selecting appropriated operating conditions. Both energetic and exergetic performance wise, CEETC and MEETC are better compared with
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VETC, but poorer compared with TETC. Second law efficiency can be improved by maximum 9% by using ejector over valve for given ranges. In view of the trade-off between the system performance and cost associated with expansion devices, the ejector may be the best alternative expansion device at least for low-capacity transcritical CO2 heat pump systems. References [1] Groll EA. Recent advances in the transcritical CO2 cycle technology. In: Eighth national and seventh ISHMT-ASME heat and mass transfer conference, IIT Guahati, India, 2006. [2] Hrnjak PS. Improvement options for CO2 and R134a systems, MAC Summit, Saalfelden, Austria, 2006. [3] Groll EA, Kim JH. Review of recent advances toward transcritical CO2 cycle technology. HVAC&R Research 2007;13(3):499–520. [4] Kornhauser AA. The use of an ejector as a refrigerant expander. In: Proceedings of the 1990 USNC/IIR-Purdue refrigeration conference, USA, 1990. p. 10–9. [5] Liu JP, Chen JP, Chen ZJ. Thermodynamic analysis on trans-critical R744 vaporcompression/ejection hybrid refrigeration cycle. In: Proceedings of the fifth IIR Gustav Lorentzen conference on natural working fluids, Guangzhou, China, 2002. p. 184–8. [6] Elbel SW, Hrnjak PS. Effect of internal heat exchanger on performance of transcritical CO2 systems with ejector. In: Proceedings of the 10th interna-
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