energies Article
Parameter Sensitivity Study for Typical Expander-Based Transcritical CO2 Refrigeration Cycles Bo Zhang
ID
, Liu Chen, Lang Liu *, Xiaoyan Zhang, Mei Wang, Changfa Ji and KI-IL Song
ID
Energy School, Xi’an University of Science and Technology, Yanta Road, Xi’an 710054, China;
[email protected] (B.Z.);
[email protected] (L.C.);
[email protected] (X.Z.);
[email protected] (M.W.);
[email protected] (C.J.);
[email protected] (K.-I.S.) * Correspondence:
[email protected]; Tel.: +86-29-8558-3143
Received: 18 April 2018; Accepted: 14 May 2018; Published: 17 May 2018
Abstract: A sensitivity study was conducted for three typical expander-based transcritical CO2 cycles with the developed simulation model, and the sensitivities of the maximum coefficient of performance (COP) to the key operating parameters, including the inlet pressure of gas cooler, the temperatures at evaporator inlet and gas cooler outlet, the inter-stage pressure and the isentropic efficiency of expander, were obtained. The results showed that the sensitivity to the gas cooler inlet pressure differs greatly before and after the optimal gas cooler inlet pressure. The sensitivity to the intercooler outlet temperature in the two-stage cycles increases sharply to near zero and then keeps almost constant at intercooler outlet temperature of higher than 45 ◦ C. However, the sensitivity stabilizes near zero when the evaporator inlet temperature is very low of −26.1 ◦ C. In two-stage compression with an intercooler and an expander assisting in driving the first-stage compressor (TEADFC) cycle, an abrupt change in the sensitivity of maximum COP to the inter-stage pressure was observed, but disappeared after intercooler outlet temperature exceeds 50 ◦ C. The sensitivity of maximum COP to the expander isentropic efficiency increases almost linearly with the expander isentropic efficiency. Keywords: parameter sensitivity; CO2 transcritical cycle; refrigeration; expander; COP
1. Introduction With the ratification of the Montreal Protocol in 1987 and the Kyoto Agreement in 1997, the search for sustainable substances for refrigeration applications has become urgent. Due to concerns about the unknown presumed unfavorable influence of various artificial refrigerants on the environment, the use of natural working fluids as refrigerants has been promoted [1]. Among various natural refrigerants, carbon dioxide was considered to be the foremost choice thanks to its many excellent engineering application advantages [2,3]. However, the relatively large throttling loss, which decreases significantly the performance of the transcritical CO2 refrigeration system, weakens considerably the competitive advantage of carbon dioxide, and recovering the power in the throttling process with the expander was hereby suggested by Lorentzen [2]. After that, different expander-based transcritical CO2 cycles were studied. Robinson et al. [4] and Yang et al. [5] analysed the performance of single-stage compression transcritical CO2 cycles with a throttling valve and with an expander. Similar findings were that the irreversibility loss of the expansion process was reduced significantly almost by 35~50% with the appliance of the expander, and the COP of the throttling valve cycle was improved by on average 25~33%.Yang et al. [6] presented that the COP of five investigated transcritical CO2 cycles with expander were all higher than that of single-stage compression with throttle valve cycle, reaching from 30.81% to 45.62% at given design
Energies 2018, 11, 1279; doi:10.3390/en11051279
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points, and the COP of two-stage compression with expander driving high-pressure stage (TCDH) cycle is the highest. Cho et al. [7] developed a numerical simulation model to evaluate the performance of improved CO2 cycles with an expander, an intercooler or a vapour injection. They concluded that three methods yielded a 28.3% (the expander efficiency of 30%), 13.1% and18.3% improvement of COP over that of the basic throttling valve cycle. It is well known that the most efficient method to improve the performance of transcritical CO2 cycle is to replace the throttling valve with an expander and recover its expansion work. Therefore, various types of CO2 expanders were developed and investigated experimentally, such as free piston expander-compressor units [8,9], scroll expander [10], rolling piston expander [11,12], vane rotary expander [13,14], reciprocating piston expander [15,16] and radial piston expander [17]. After more than ten years of continuous development and improvement, the isentropic efficiency of expander was greatly improved, reaching a maximum of 77% [12]. However, a successful application of expander in the market for transcritical CO2 cycle products has not been reported. In subcritical conditions, the CO2 cycle works similarly as traditional Freon systems, as its high-side pressure and temperature are not independent in the two-phase region. So the experience in Freon systems can be used for reference. When the external temperature exceeds the CO2 critical temperatures of 30.85 ◦ C, the transcritical CO2 cycle must be adopted to overcome this shortcoming. Unlike the subcritical vapour compression cycles, the high-side pressure and temperature of transcritical CO2 cycle are independent and affected each other in operation, which increases the difficulty of operating condition control. The opening degree of throttling valve can be controlled accurately and rapidly, such as electronic expansion and electronic backpressure valves, which were suitable to regulate the operation of transcritical CO2 plants and applied widely in the market. In the experiment of evaluating a model-free real-time optimization and control strategy proposed by Peñarrocha et al., two electronic expansion valves (controlled by a PI controller) carried on the precise real-time control to the high-side pressure according to the feedback signal of compression power [18]. However, it is difficult for an expander. The driving force of expander only comes from the high and low pressure difference of transcritical CO2 cycle. The interaction among many factors involved in the operation of expander, such as the pressure difference between high side and low side, the inlet temperature of expander, the consumption of expansion work, the mass flow rate, is bound to lead to weak regulation ability that restricts its popularization to the market. Therefore, the quantification of working characteristics for transcritical CO2 in different parameters is needed to find the appropriate control accuracy or method. Many researchers, such as Robinson [4], Yang [5,6], Cho [7], Cecchinato [19], have studied the effects of parameters on COP for different transcritical CO2 cycles including single- and two-stage cycles with or without an expander. However, only trends of COP variations with parameters are presented. It is necessary to understand the effect extent of parameters on the CO2 cycle performance, which are essential on the operation control and design of the CO2 systems. Therefore, in this paper, a quantitative analysis of the effect of parameters on COP is done by relative sensitivity in three typical expander-based transcritical CO2 cycles. 2. Three Typical Expander-Based Transcritical CO2 Cycles In theory, the throttling valve in all the existing transcritical CO2 refrigeration systems can be replaced by an expander, but only three typical expander-based transcritical CO2 cycles that are widely used and studied in the published literatures are investigated in the current study. 2.1. Single-Stage Compression with an Expander (SE) The SE cycle is the most basic and simplest configuration for replacing the throttling valve with an expander. Its performance has been studied based on the first and second laws of thermodynamics [4,5] and adopted in developed CO2 expander prototype test rigs [10,15]. The schematic diagram of the SE and the corresponding P-h diagram are shown in Figure 1. An obvious characteristic of SE cycle is
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that the expander is connected to the compressor via a motor, and therefore the expansion work is recovered to provide assistance in driving the compressor. However, high discharge temperatures, even more than 150 ◦ C, are associated with high gas cooler exit temperatures, and/or low evaporating temperatures and low isentropic compression efficiencies [20]. This may reduce the reliability of compressor in xpractical due to the deterioration of its lubrication conditions. Energies 2018, 11, FOR PEERapplications REVIEW 3 of 19 13.0
2
3 10.0
2
Gas cooler
P / MPa
3
Compressor
5.0
Expander
Evaporator
4
1
4
1
3.0 200
250
300
350
-1
400
450
500
h / kJ.kg
(a)
(b)
Figure 1. of of SESE cycle andand the the corresponding P-h diagram. (a) Schematic diagram;diagram; (b) P-h Figure 1. Schematic Schematic cycle corresponding P-h diagram. (a) Schematic diagram. (b) P-h diagram.
2.2. Two-Stage Compression with an Intercooler and an Expander Driving the Second-Stage Compressor 2.2. Two-Stage Compression with an Intercooler and an Expander Driving the Second-Stage Compressor (TEDSC) (TEDSC) The use of two-stage compression cycle with an intercooler is an efficient measure to improve the The use of two-stage compression cycle with an intercooler is an efficient measure to improve cycle COP by decreasing the irreversible losses in the compression process [21]. Replacing the throttling the cycle COP by decreasing the irreversible losses in the compression process [21]. Replacing the valve with an expander for power recovery can further improve the cycle COP significantly owing throttling valve with an expander for power recovery can further improve the cycle COP significantly to the decreased irreversible losses in the throttling process. To effectively utilize the work extracted owing to the decreased irreversible losses in the throttling process. To effectively utilize the work from the expansion process, the compressor should be coupled with the expander directly. JL Yang’s extracted from the expansion process, the compressor should be coupled with the expander directly. research results showed that the COP of two-stage compression cycle with an expander to drive the JL Yang’s research results showed that the COP of two-stage compression cycle with an expander to low-pressure compressor was smaller than to drive the high-pressure compressor, even smaller than drive the low-pressure compressor was smaller than to drive the high-pressure compressor, even that of SE cycle [6]. Therefore, the two-stage cycle with an intercooler and an expander driving the smaller than that of SE cycle [6]. Therefore, the two-stage cycle with an intercooler and an expander second-stage compressor (TEDSC) is usually adopted [8]. driving the second-stage compressor (TEDSC) is usually adopted [8]. The schematic and corresponding P-h diagrams of TEDSC cycle are shown in Figure 2. To avoid The schematic and corresponding P-h diagrams of TEDSC cycle are shown in Figure 2. To avoid CO2 refrigerant from leaking to external environment and reduce transmission losses of expansion CO2 refrigerant from leaking to external environment and reduce transmission losses of expansion work, the expander and the second-stage compressor were usually combined into one unit by a work, the expander and the second-stage compressor were usually combined into one unit by a common shaft, like as the prototypes developed by Nickl et al. [8] and Zhang et al. [9]. Therefore, common shaft, like as the prototypes developed by Nickl et al. [8] and Zhang et al. [9]. Therefore, they run at a same speed rate, and the power required by the second-stage compressor is supplied they run at a same speed rate, and the power required by the second-stage compressor is supplied entirely by the expander. The inter-stage pressure in this cycle is a function of their coupling operation, entirely by the expander. The inter-stage pressure in this cycle is a function of their coupling which may deviate from optimal values in various actual working conditions. In addition, the huge operation, which may deviate from optimal values in various actual working conditions. In addition, pressure difference between the expander and the second-stage compressor has challenged the seal of the huge pressure difference between the expander and the second-stage compressor has challenged the common shaft. the seal of the common shaft. 13.0
4
Gas cooler
5
10.0
4 2
5
2nd Compressor
Expander
P / MPa
3
3
Intercooler
5.0
2 1st Compressor
6
6 Evaporator
1
3.0 200
250
1 300
350
400
450
500
-1
h / kJ.kg
(a)
(b)
Figure 2. Schematic of TEDSC cycle and the corresponding P-h diagram. (a) Schematic diagram; (b) P-h diagram.
common shaft, like as the prototypes developed by Nickl et al. [8] and Zhang et al. [9]. Therefore, they run at a same speed rate, and the power required by the second-stage compressor is supplied entirely by the expander. The inter-stage pressure in this cycle is a function of their coupling operation, which may deviate from optimal values in various actual working conditions. In addition, the huge pressure Energies 2018, 11, 1279 difference between the expander and the second-stage compressor has challenged 4 of 20 the seal of the common shaft. 13.0
5
10.0
4
Gas cooler
4 2
P / MPa
3
5
2nd Compressor
Expander
3
Intercooler
5.0
2 1st Compressor
6
6
3.0 200
1
Evaporator
1
250
300
350
400
450
500
-1
h / kJ.kg
(a)
(b)
Figure of of TEDSC cycle andand the the corresponding P-h diagram. (a) Schematic diagram; (b) P-h Figure 2.2.Schematic Schematic TEDSC cycle corresponding P-h diagram. (a) Schematic diagram; diagram. (b) P-h diagram.
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Two-Stage Compression with an Intercooler and an Expander 2.3. Two-Stage Expander Assisting Assisting in in Driving Driving the the First-Stage First-Stage Compressor (TEADFC) (TEADFC) Compressor Figure 33shows showsthe theschematic schematic diagram corresponding P-h diagram the TEADFC Figure diagram andand the the corresponding P-h diagram of theof TEADFC cycle, cycle, which was suggested by Yang In this cycle, expander assistsinindriving driving the the first-stage first-stage which was suggested by Yang [6]. [6]. In this cycle, thethe expander assists compressor through throughaamotor, motor,which whichmeans meansanan additional power supplied to freely adjust compressor additional power cancan be be supplied to freely adjust the the speed of first-stage compressor without any restriction from the expander, so the advantage of speed of first-stage compressor without any restriction from the expander, so the advantage of this this cycle is that optimal inter-stage pressure guaranteedbybythe thecoordination coordinationof of firstfirst- and and cycle is that the the optimal inter-stage pressure cancan bebe guaranteed second-stage compressors in wide operation conditions. But the utilization efficiency of expansion second-stage compressors in wide operation conditions. But the utilization efficiency of expansion work is is obviously obviously reduced reduced due work due to to large large losses losses caused caused by by the the addition addition of of intermediate intermediate links. links. 13.0
4
5
10.0
5 2nd Compressor Intercooler
3 2
4
P / MPa
Gas cooler
2
3
5.0 1st Compressor
Expander
6
6 Evaporator
1
3.0 200
250
1 300
350
400
450
500
-1
h / kJ.kg
(a)
(b)
Figure the corresponding P-hP-h diagram. (a) Schematic diagram; (b) Figure 3. 3. Schematic SchematicofofTEADFC TEADFCcycle cycleand and the corresponding diagram. (a) Schematic diagram; P-h diagram. (b) P-h diagram.
3. Simulation Model 3. Simulation Model Three typical expander-based transcritical CO2 systems were modelled by applying the energy Three typical expander-based transcritical CO2 systems were modelled by applying the energy conservation to all the components of the system, typically including the compressor, expander, gas conservation to all the components of the system, typically including the compressor, expander, cooler and evaporator. Each component was treated as a control volume. The following assumptions gas cooler and evaporator. Each component was treated as a control volume. The following were made as the simulation model was established: assumptions were made as the simulation model was established: (i) The thermodynamic processes in all of the components are steady-state ones, and the kinetic and potential energies are negligible. (ii) The compression process is non-isentropic, and its isentropic efficiency is given by an empirical correlation. (iii) The state at the evaporator outlet is saturated. (iv) The heat loss and pressure drops in the piping connecting the components are negligible. (v) Heat transfer between the components and the ambient are not accounted for.
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(i)
The thermodynamic processes in all of the components are steady-state ones, and the kinetic and potential energies are negligible. (ii) The compression process is non-isentropic, and its isentropic efficiency is given by an empirical correlation. (iii) The state at the evaporator outlet is saturated. (iv) The heat loss and pressure drops in the piping connecting the components are negligible. (v) Heat transfer between the components and the ambient are not accounted for. The isentropic efficiency of the expander is taken to be 0.6 according to the reports [5,9,12]. 3.1. Refrigeration Capacity in the Evaporator The specific refrigeration capacity equations for the three cycles were as follows: qev(SE) = h1 − h4
(1)
qev(TESC) = qev(TEAC) = h1 − h6
(2)
3.2. Input Work and Isentropic Efficiency of the Compressor The input work of each cycle can be calculated using the following formula: wc(SE) = h2 − h1
(3)
wc(TESC) = wc(TEAC) = (h2 − h1 ) + (h4 − h3 )
(4)
For the TEDSC cycle, the input work of the second-stage compressor was calculated firstly according to the assumed inter-stage pressure in the given conditions. Then it was checked to see if the value agreed with the output work of the expander. If not, a new calculation was carried out after altering the inter-stage pressure. The trial calculation continued until the input work of the second-stage compressor coincided with the expander output work, and then the input work of the compressors could be acquired. The isentropic efficiency of the compressor was used to calculate the compression work as follows: ηis,c(SE) =
his,2 − h1 h2 − h1
(5)
ηis, f sc(TESC,TEAC) =
his,2 − h1 h2 − h1
(6)
ηis,ssc(TESC,TEAC) =
his,4 − h3 h4 − h3
(7)
where, ηis was calculated from the following correlation [4]: ηis = 0.815 + 0.022
Pdis,c Psuc,c
− 0.0041
Pdis,c Psuc,c
2
+ 0.0001
Pdis,c Psuc,c
3 (8)
3.3. Output Work of the Expander The output work of expander in each cycle was obtained as follows: we(SE) = h3 − h4
(9)
we(TESC) = we(TEAC) = h5 − h6
(10)
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3.4. Coefficient of Performance If CO2 state at each point in the transcritical CO2 cycles is known, the COP of the considered cycles can be obtained by: qev COP = (11) wc − we 3.5. Calculation of the Maximum COP The previous research results showed that the optimal high side pressure and the optimal inter-stage pressure exist for the expander-based transcritical CO2 cycles [4,6]. For the SE cycle, an iterations of calculating COP was carried using dichotomy method for the gas cooler inlet pressure from 8 MPa to 14 MPa to find its maximum COP under a certain working conditions. In TEDSC cycle, the speed ratio of the second-stage compressor to the expander was constant when the components in the cycle were determined, as described in Yang’s statements [6]. During the operation, the mass flow rate through the first-stage compressor, the second-stage compressor and the expander was equivalent, meanwhile the power consumption of the second-stage compressor was limited by the output work of the expander. As a result, the inter-stage pressure was determined when the gas cooler inlet pressure was fixed at given temperatures at evaporator inlet and gas cooler outlet. Therefore, two nested iterations were required to calculate the maximum COP. In the outer iterations, the gas cooler inlet pressure was supposed increasing gradually from 8 MPa to 14 MPa. In the inner iterations, the inter-stage pressure was calculated using the dichotomy method based on mass flow conservation and energy conservation between the expander and the second-stage compressor. By comparing the COP got in each loop, the maximum COP was gained. In the TEADFC cycle, the expander was not combined with the first-stage compressor, so the inter-stage pressure could be adjusted when the gas cooler inlet pressure was determined. Therefore, two nested iterations were also implemented to find the maximum COP. In the first loop, the gas cooler inlet pressure was supposed gradually increasing from 8 MPa to 14 MPa. In the second loop, a provisional maximum COP was calculated increasing the inter-stage pressure from the outlet pressure of evaporator to the gas cooler inlet pressure on the basis of mass flow conservation. During the calculation, the provisional maximum COP was continuously replaced by higher one. Finally, the maximum COP could be obtained. 3.6. Relative Sensitivity Thermodynamic analysis on transcritical CO2 cycles was commonly done by the curves of COP versus the considered parameters, which can directly and clearly reflect their performance. However, the impact amplitude of parameters on COP can only be judged roughly by the slope of curves, which makes it difficult to rank the influence of different parameters on COP. Therefore, the relative sensitivity defined by Equation (12) was applied in the current study. It is a dimensionless quantity that facilitates the comparison between the influences of considered parameters [22]: ∂ ln(COPi ) S= ∂ ln( xi )
= x =i,0
∂COPi /COPi,0 ∂xi /xi,0
i = 1, 2, . . . , n
(12)
where, xi are the operating parameters of concern, xi,0 are the parameter values at the baseline state point, and COPi,0 is the coefficient of performance at the baseline state point. It should be noted that the Kelvin scale was used for the temperature. From the above definition, it can be seen that the higher the relative sensitivity is, the greater the effect of the parameter on the COP has. Furthermore, the parameter has a positive effect on the COP when its sensitivity is greater than zero, and vice versa. Optimum COP appears as the parameter sensitivity is equal to zero. Therefore, the relative sensitivity indicates how the COP of the cycle is sensitive to the varied parameter.
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3.7. Calculation of CO2 Thermodynamic Properties The simulation programs for the mentioned expander-based transcritical CO2 cycles were developed in FROTRAN (Version 6.5, Compaq, Houston, TX, USA) language. The evaluation of CO2 thermodynamic property was carried out using the subroutines of the NIST REFPROP 9.0 FORTRAN (Version 9.0, NIST, Gaithersburg, MD, USA) code [23]. However, the calculation of CO2 thermodynamic property at some points near the critical point may be unstable. So many discrete property values in a zone near the critical point (7 MPa < P < 8 MPa, 28 ◦ C < T < 38 ◦ C) were calculated in advance using Engineering Equation Solver (EES) [24]. The CO2 property values were calculated by interpolation in this region, whose errors were less than 0.1% compared with the EES calculated data. 4. Results and Discussion For the three typical expander-based transcritical CO2 cycles (SE, TEDSC and TEADFC), a simulation model was developed to obtain maximum COP, and then the parameter sensitivity analysis on maximum COP was conducted. According to [5] and considering the application area of transcritical CO2 refrigeration cycle, such as refrigerator and air conditioning. The relative sensitivities were obtained at various evaporator inlet temperatures (from −26.1 ◦ C to 21.1 ◦ C), gas cooler outlet temperatures (from 30 ◦ C to 50 ◦ C) and gas cooler inlet pressures (from 8 MPa to 14 MPa). When calculating the sensitivity of a parameter, other parameters remain unchanged exclude gas cooler inlet pressure and inter-stage pressure. The purpose of this is to avoid the influences from the variations of other parameters. The results regarding the sensitivity of maximum COP to the operating conditions are discussed as follows. 4.1. Sensitivity of Maximum COP to Gas Cooler Inlet Pressure Figure 4 shows the changes of COP as well as its sensitivity to the gas cooler inlet pressure versus the gas cooler inlet pressure at various gas cooler outlet temperatures or evaporator inlet temperatures. It can be seen that the variations of sensitivity have the same trend for the three typical cycles. The optimal gas cooler inlet pressure is a critical point, which divides the range of gas cooler inlet pressure into two parts. Before the optimal gas cooler inlet pressure, the sensitivity varies greatly with an increase in the gas cooler inlet pressure, and after the gas cooler inlet pressure exceeds the optimal value, the sensitivity keeps almost constant approaching zero. As shown in Figure 4a, at the given evaporator inlet temperature of 5 ◦ C and gas cooler outlet temperature of 35 ◦ C, the sensitivity drops sharply from about 10 to zero as the gas cooler inlet pressure increases from 8 MPa to the optimal pressure of about 9.2 MPa. After that, the sensitivity changes little between zero and −0.8. However, as the gas cooler outlet temperature increases to 30 ◦ C, the sensitivity only varies in a small range of −1.1~−0.4 in the whole calculation range of the gas cooler inlet pressure, which implies that the optimal gas cooler inlet pressure is smaller than 8 MPa as the gas cooler outlet temperature exceeds 30 ◦ C. From Figure 4, significant influences of temperatures both at the gas cooler outlet and at the evaporator inlet on the sensitivity can be observed. However, the effects of temperatures on the sensitivities become weak after the gas cooler inlet pressure exceeds the optimal value.
°C, the sensitivity only varies in a small range of −1.1~−0.4 in the whole calculation range of the gas cooler inlet pressure, which implies that the optimal gas cooler inlet pressure is smaller than 8 MPa as the gas cooler outlet temperature exceeds 30 °C. From Figure 4, significant influences of temperatures both at the gas cooler outlet and at the Energies 2018, 11, 1279 on the sensitivity can be observed. However, the effects of temperatures on 8the of 20 evaporator inlet sensitivities become weak after the gas cooler inlet pressure exceeds the optimal value. 40
S
Tout,gc= 35℃
Tout,gc= 30℃
30
SE TEDSC TEADFC
SE TEDSC TEADFC
SE TEDSC TEADFC
20
Tout,gc= 50℃
Tin,evap = 5℃
10
0 6
Maximum COP
5 4 3 2 1 0 8
9
10
11
12
13
14
Pin,gc / MPa Energies 2018, 11, x FOR PEER REVIEW
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(a)
20
S
SE TEDSC TEADFC
SE TEDSC TEADFC
SE TEDSC TEADFC
10
Tin,evap= 21.1℃
Tin,evap= 5℃
Tin,evap= −26.1℃
15
Tout,gc = 35℃
5
0
Maximum COP
10
8
6
4
2
0 8
9
10
11
12
13
14
Pin,Gc / MPa
(b) Figure 4. Sensitivity of maximum COP to gas cooler inlet pressure (a) Tin,evap = 5 °C; (b) Tout,gc = 35 °C. Figure 4. Sensitivity of maximum COP to gas cooler inlet pressure (a) Tin ,evap = 5 ◦ C; (b) Tout,gc = 35 ◦ C.
There was a difference in the optimal high-side pressure of transcritical CO2 cycle for the nonideal compression and ideal compression. As an evaporating temperature is greater than 0 °C, the optimal pressure for non-ideal compression could be marginally higher than that for the ideal case, according to a thermodynamic basis provided by Srinivasan et al. [20]. Since the optimal COP is much more sensitive to the gas cooler inlet pressure before the optimal gas cooler inlet pressure than after the optimal value, the high-side pressure of the transcritical CO2 system should be a little higher than
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There was a difference in the optimal high-side pressure of transcritical CO2 cycle for the non-ideal compression and ideal compression. As an evaporating temperature is greater than 0 ◦ C, the optimal pressure for non-ideal compression could be marginally higher than that for the ideal case, according to a thermodynamic basis provided by Srinivasan et al. [20]. Since the optimal COP is much more sensitive to the gas cooler inlet pressure before the optimal gas cooler inlet pressure than after the optimal value, the high-side pressure of the transcritical CO2 system should be a little higher than the calculated optimal value so that the actual COP approaches the optimal one if the calculation uncertainties are taken into account. 4.2. Sensitivity of Maximum COP to Evaporator Inlet Temperature Figure 5 displays the variation of maximum COP as well as its sensitivity to the evaporator inlet temperature as the inlet temperature of evaporator increases. The trend of sensitivity variation is almost the same for the three typical cycles. Gradually faster increase in the sensitivity can be observed as the temperature at the evaporator inlet increases. As the evaporator inlet temperature increases from −25 ◦ C to 21 ◦ C, the sensitivity increases from 6.1 to 26.1 at the gas cooler outlet temperature of 30 ◦ C and from 6.4 to 17.5 at the gas cooler outlet temperature of 35 ◦ C. This indicates that the evaporator inlet temperature has a larger effect on the maximum COP at a higher evaporator Energies 2018, 11, x FOR PEER REVIEW 9 of 19 inlet temperature. 30 25
S
20 15 10 5
16
Tout,gc =30 ℃
Maximum COP
14
35 ℃
SE TEDSC TEADFC
12 10
SE TEDSC TEADFC
Tout,ic = 50 ℃
8 6 4 2 -30
-25
-20
-15
-10
-5
0
Tin,evap / ℃
5
10
15
20
25
Figure 5. Sensitivity of maximum COP to temperature at the evaporator inlet. inlet.
4.3. Sensitivity of Maximum COP to Gas Cooler Outlet Temperature Temperature Figure 6 gives the variation of maximum COP as well as its sensitivity to the gas cooler outlet outlet temperature temperature increases. The sensitivity is negative and increases temperature as the gas cooler outlet with the thegas gas cooler outlet temperature. Smaller absolute of sensitivity occursevaporator at lower with cooler outlet temperature. Smaller absolute value ofvalue sensitivity occurs at lower evaporator inlet temperature for all the three typical cycles, which means that influence of gas inlet temperature for all the three typical cycles, which means that influence of the gas coolerthe outlet cooler outlet temperature on theCOP maximum COP smaller at lower evaporator inlet temperature and temperature on the maximum is smaller atislower evaporator inlet temperature and decreases decreases with gradually with the gas increased cooler outlet temperature. gradually the increased cooler gas outlet temperature. -4 -6 -8
S
-10 -12 -14 -16
Figure 6 gives the variation of maximum COP as well as its sensitivity to the gas cooler outlet temperature as the gas cooler outlet temperature increases. The sensitivity is negative and increases with the gas cooler outlet temperature. Smaller absolute value of sensitivity occurs at lower evaporator inlet temperature for all the three typical cycles, which means that influence of the gas Energies outlet 2018, 11,temperature 1279 10 and of 20 cooler on the maximum COP is smaller at lower evaporator inlet temperature decreases gradually with the increased gas cooler outlet temperature. -4 -6 -8
S
-10 -12 -14 -16 -18 -20
Tin,evap = −26.1 ℃
Maximum COP
5
5℃
SE TEDSC TEADFC
4
SE TEDSC TEADFC
3
Tout,ic = 50 ℃ 2
1 30
35
40
Tout,gc / ℃
45
50
Figure 6. Sensitivity Sensitivity of of maximum maximum COP to temperature at gas cooler outlet.
From Figure 6, the deviation of sensitivity between at evaporator inlet temperatures of −26.1 ◦ C and at 5 ◦ C reduces from 9.0 to 1.4 for the two-stage cycles (TEDSC and TEADFC) and from 7.6 to 0.8 for the sing-stage cycle (SE) as the gas cooler outlet temperature increases from 31 ◦ C to 50 ◦ C. This suggests that the sensitivity of the maximum COP to the gas cooler outlet temperature approaches gradually at higher gas cooler outlet temperature for various evaporator inlet temperatures. From Figure 6 it can also be found that the sensitivity for TEDSC and TEADFC cycles are very close and the absolute values are smaller than that of SE. In the calculation range of gas cooler outlet temperature, the absolute value of sensitivity of the two-stage cycles is 2.8 and 2.3 on average lower than that of the single-stage cycle at evaporator inlet temperatures of −26.1 ◦ C and 5 ◦ C. As a result, the gas cooler outlet temperature has a smaller effect on the maximum COP in the two-stage cycle than in the single-stage cycle. 4.4. Sensitivity of Maximum COP to Pressure Losses through Gas Cooler and Evaporator Figure 7 describes the variation of maximum COP as well as its sensitivity to the pressure losses through the gas cooler and evaporator versus the pressure drop through the gas cooler and evaporator. It is obvious that sensitivity changes linearly with the pressure drop with a negative slope. As the pressure drop increases, the sensitivity of the maximum COP to the pressure loss through the evaporator decreases much faster than through the gas cooler. Moreover, with the sensitivity of the three cycles compared, it can be found that the sensitivities for TEDSC and TEADFC cycles are very close and the sensitivity of SE reduces faster with the increased pressure loss, especially through the gas cooler. With the same pressure loss of 1 MPa, the absolute value of the sensitivity for SE cycle is approximately 7% and 160% higher than that of TEDSC and TEADFC cycles through the evaporator and the gas cooler, respectively.
slope. As the pressure drop increases, the sensitivity of the maximum COP to the pressure loss through the evaporator decreases much faster than through the gas cooler. Moreover, with the sensitivity of the three cycles compared, it can be found that the sensitivities for TEDSC and TEADFC cycles are very close and the sensitivity of SE reduces faster with the increased pressure loss, especially through the gas cooler. With the same pressure loss of 1 MPa, the absolute value of the Energies 2018, 11, 1279 11 of 20 sensitivity for SE cycle is approximately 7% and 160% higher than that of TEDSC and TEADFC cycles through the evaporator and the gas cooler, respectively. 0.1 0.0
S
-0.1 -0.2 -0.3 -0.4 -0.5
Tin,evap= 5℃
Maximum COP
5.0
Tout,gc=Tout,ic= 35℃
4.5
4.0
Ploss,evap
Ploss,gc
SE TEDSC TEADFC
3.5
3.0 0.0
0.1
0.2
SE TEDSC TEADFC 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Ploss / MPa
Figure 7. Sensitivity maximumCOP COPto to pressure pressure losses gasgas cooler andand evaporator. Figure 7. Sensitivity of of maximum lossesthrough through cooler evaporator.
4.5. Sensitivity of Maximum COP to Isentropic Efficiency of Expander
4.5. Sensitivity of Maximum COP to Isentropic Efficiency of Expander As many studies stated, the isentropic efficiency of expander plays an important role in
As many studies stated, the isentropic efficiency of expander plays an important role in improving improving COP of the transcritical CO2 cycle. From Figure 8, it can be observed that the sensitivity of COP maximum of the transcritical CO2isentropic cycle. From Figureof 8, it can be observed the sensitivity of maximum COP to the efficiency expander increases that linearly with the increasing COP isentropic to the isentropic efficiency of expander increases linearly with the increasing isentropic of expander. The slope of the sensitivity keeps almost the same at various Energies 2018,efficiency 11, x FOR PEER REVIEW 11 efficiency of 19 of expander. The slope of the sensitivity keeps almost the same at various evaporator inlet temperatures, evaporator temperatures, steeper increase trendatofhigher the sensitivity is observed at higher whereas steeperinlet increase trend ofwhereas the sensitivity is observed gas cooler outlet temperature. gas cooler outlet temperature. The sensitivity curves for SE and TEADFC are very close, but the sensitivity for TEDSC is more The sensitivity curves for SE and TEADFC are very close, but the sensitivity for TEDSC is more modest. This is caused by the fact that the inter-stage pressure, determined by the isentropic efficiency modest. This is caused by the fact that the inter-stage pressure, determined by the isentropic of expander in TEDSC, departs from the optimal inter-stage pressure. efficiency of expander in TEDSC, departs from the optimal inter-stage pressure. 0.6 0.5
S
0.4 0.3 0.2 0.1 0.0
Maximum COP
5
4
Tin,evap= −26.1℃ 3
5℃
SE TEDSC TEADFC
Tout,gc=35℃ Tout,ic=50℃
SE TEDSC TEADFC
2
1 0.1
0.2
0.3
0.4
0.5
is,ed
0.6
0.7
(a) 0.9 0.8 0.7
S
0.6 0.5 0.4 0.3 0.2 0.1 0.0 2.6
Tout,gc=30℃ SE TEDSC TEADFC
50℃
Tin,evap= −26.1℃
Figure 8. Cont. SE TEDSC TEADFC
Tout,ic= 50℃
0.8
0.9
1.0
M
TEDSC TEADFC
Tout,ic=50℃
TEDSC TEADFC
2
1 0.1
Energies 2018, 11, 1279
0.2
0.3
0.4
0.5
is,ed
0.6
0.7
0.8
0.9
0.8
0.9
1.0
12 of 20
(a) 0.9
Tout,gc=30℃
0.8
0.6
S
50℃
SE TEDSC TEADFC
0.7
0.5
Tin,evap= −26.1℃ SE TEDSC TEADFC
Tout,ic= 50℃
0.4 0.3 0.2 0.1 0.0 2.6
Maximum COP
2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.1
0.2
0.3
0.4
0.5
is,ed
0.6
0.7
1.0
(b) Figure 8. 8. Sensitivity Sensitivity of of maximum maximumCOP COPtotoisentropic isentropicefficiency efficiencyofofexpander expander different temperature Figure (a)(a) different temperature at at evaporator inlet; (b) different temperature at gas cooler outlet. evaporator inlet; (b) different temperature at gas cooler outlet.
4.6. Sensitivity of Maximum COP to Temperature at Intercooler Outlet 4.6. Sensitivity of Maximum COP to Temperature at Intercooler Outlet Figure 9 shows the maximum COP as well as its sensitivity to the intercooler outlet temperature Figure 9 shows the maximum COP as well as its sensitivity to the intercooler outlet temperature as the temperature at intercooler outlet increases. The sensitivity is less than zero, which means that as the temperature at intercooler outlet increases. The sensitivity is less than zero, which means temperature at intercooler outlet has a negative effect on the maximum COP. From Figure 9a it can be that temperature at intercooler outlet has a negative effect on the maximum COP. From Figure 9a it can be seen that the sensitivity increases sharply from a low value to nearly zero as the intercooler outlet temperature increases from 35 ◦ C to 45 ◦ C, but there is a marginal variation in sensitivity as the temperature changes from 45 ◦ C to 80 ◦ C at various evaporator inlet temperatures. However, the sharp change of sensitivity becomes weak and disappears finally with the decreased evaporator inlet temperature. For example, at the evaporator inlet temperature of −26.1 ◦ C, the sensitivity varies from −1.1 to −0.4 as the intercooler outlet temperature changes from 35 ◦ C to 80 ◦ C. Figure 9b presents the variation maximum COP as well as its sensitivity to the intercooler outlet temperature at various gas cooler outlet temperatures as the evaporator temperature is kept at −26.1 ◦ C. A slight increase of sensitivity is observed over the calculation range of intercooler outlet temperature.
change of sensitivity becomes weak and disappears finally with the decreased evaporator inlet temperature. For example, at the evaporator inlet temperature of −26.1 °C, the sensitivity varies from −1.1 to −0.4 as the intercooler outlet temperature changes from 35 °C to 80 °C. Figure 9b presents the variation maximum COP as well as its sensitivity to the intercooler outlet temperature at various gas cooler 2018, outlet as the evaporator temperature is kept at −26.1 °C. A slight increase Energies 11, temperatures 1279 13 of of 20 sensitivity is observed over the calculation range of intercooler outlet temperature. 0 -2 -4
TEADFC Tout,gc =35℃
TEDSC
-6
S
Tin,evap= −26℃
-8
Tin,evap= 5℃
-10
Tin,evap= 21.1℃
-12 -14 10
Maximum COP
9 8 7 6 5 4 1.8 1.6 35
40
45
50
55
60
65
70
75
80
Tout,ic / ℃
(a) 0.0 -0.2 -0.4
S
-0.6 -0.8 -1.0 -1.2 -1.4 -1.6 2.4 2.3
Maximum COP
2.2 2.1
TEDSC TEADFC
2.0
Tin,evap = −26.1℃
1.9 1.8
Tout,gc= 30℃
1.7
Tout,gc= 35℃
1.6
Tout,gc= 50℃
1.5 1.4 1.3 30
40
50
Tout,ic / ℃
60
70
80
(b) Figure 9. Sensitivity of maximum COP to temperature at intercooler outlet (a) different temperature Figure 9. Sensitivity of maximum COP to temperature at intercooler outlet (a) different temperature at at evaporator inlet; (b) different temperature at gas cooler outlet. evaporator inlet; (b) different temperature at gas cooler outlet.
The above analysis shows that the intercooler outlet temperature has little effect on the maximum COP when the intercooler outlet temperature is higher than 45 ◦ C or evaporator inlet temperature is very low. As a result, in order to improve the maximum COP effectively, the intercooler outlet temperature should be decreased at least lower than 45 ◦ C for the two-stage cycles.
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The above analysis shows that the intercooler outlet temperature has little effect on the maximum COP when the intercooler outlet temperature is higher than 45 °C or evaporator inlet temperature is very low. As1279 a result, in order to improve the maximum COP effectively, the intercooler 14outlet Energies 2018, 11, of 20 temperature should be decreased at least lower than 45 °C for the two-stage cycles.
4.7. 4.7. Sensitivity Sensitivity of of Maximum Maximum COP COPto toInter-Stage Inter-StagePressure Pressurein inTEADFC TEADFCCycle Cycle The Theinter-stage inter-stagepressure pressureisisan animportant importantparameter parameterto tobe be optimized optimizedfor for the the two-stage two-stage transcritical transcritical CO cycle. Figures 10–17 present the variations of maximum COP as well as its sensitivity the CO22 cycle. Figures 10–17 present the variations of maximum COP as well as its sensitivity to thetointerinter-stage pressure at different operating parameters, including the evaporator temperature, stage pressure at different operating parameters, including the evaporator inletinlet temperature, gas gas cooler outlet temperature, intercooler outlet temperature cooler inlet pressure. cooler outlet temperature, intercooler outlet temperature andand gasgas cooler inlet pressure. As As shown shown in in Figure Figure 10, 10,aaslow slowdecrease decreasein inthe thesensitivity sensitivityof ofmaximum maximumCOP COPwith withthe theincreased increased inter-stage inter-stagepressure pressureisisobserved, observed,and andthen thenaasharp sharp increase increaseoccurs occursat at the the inter-stage inter-stagepressure pressureof ofabout about 8.0 MPa, followed by a quick decrease to a negative value. Finally a slight variation of sensitivity 8.0 MPa, followed by a quick decrease to a negative value. Finally a slight variation of sensitivity isis observed pressure increases. The The abrupt change in thein sensitivity may lead to double observedasasthe theinter-stage inter-stage pressure increases. abrupt change the sensitivity may lead to ◦ peaks ofpeaks the maximum COP, such as the plot at the evaporator temperature of −26.1of C, which cause double of the maximum COP, such as the plot at the evaporator temperature −26.1 °C, which some obstacles to optimize the inter-stage pressure. Furthermore, the absolute value of the sensitivity cause some obstacles to optimize the inter-stage pressure. Furthermore, the absolute value of the decreases the reducing inlet temperature, and the amplitude of the abrupt sensitivitywith decreases with theevaporator reducing evaporator inlet temperature, and the amplitude of thechange abrupt decreases as well. as From Figure it can10, also be found the that location of the abrupt change decreases well. From10, Figure it can also bethat found the location of the change abrupt almost change has no relations with thewith evaporator inlet temperature. almost has no relations the evaporator inlet temperature. Tin,evap= −26℃
1.0
Tin,evap= −15℃ Tin,evap= 5℃
S
0.5
Tout,ic=Tout,gc=35℃
0.0
Pin,gc=10 MPa
-0.5 -1.0 4.5
Maximum COP
4.0
2.4 2.2 2.0 1.8 1.6 3
4
5
6
7
8
9
10
Pdis,fsc / MPa
Figure 10. 10. Sensitivity Sensitivity of of COP COP to to inter-stage inter-stage pressure pressureat atvarious variousevaporator evaporatorinlet inlettemperatures. temperatures. Figure
Figure 11 presents the variation rates of the specific compression work for the first- and secondFigure 11 presents the variation rates of the specific compression work for the first- and stage compressor at various evaporator inlet temperatures. A sudden change in the change rate of second-stage compressor at various evaporator inlet temperatures. A sudden change in the change the second-stage specific compression work occurs, which thereby causes the sharp change of the rate of the second-stage specific compression work occurs, which thereby causes the sharp change of sensitivity. From Figure 11, it can be seen that the change rate for first-stage specific compression the sensitivity. From Figure 11, it can be seen that the change rate for first-stage specific compression work increase with the decreased evaporator inlet temperature, and the change rate of the secondwork increase with the decreased evaporator inlet temperature, and the change rate of the second-stage stage specific compression work has the same trend but decreases faster. At lower evaporator inlet specific compression work has the same trend but decreases faster. At lower evaporator inlet temperature, the change rate of the first-stage compression work increases, and the effect of the temperature, the change rate of the first-stage compression work increases, and the effect of the second-stage compression work on COP is weaker. Generally, the sudden change in the change rate second-stage compression work on COP is weaker. Generally, the sudden change in the change rate of of the second-stage specific compression work can be attributed to the phenomenon of the pseudothe second-stage specific compression work can be attributed to the phenomenon of the pseudo-critical critical temperature of CO2. temperature of CO2 .
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20 20
Tin,evap= −26℃ Tin,evap= −26℃ Tin,evap= −15℃ T ,evap= −15℃ Tinin,evap = 5℃ Tin,evap= 5℃ Tout,gc= 35℃ T = 35℃ Pinout,gc,gc= 10 MPa Pin,gc= 10 MPa
nd
2 nd Compressor 2 Compressor
-1
-1 -1 MPa w|/ Pdis,fsc kgkgMPa / kJ/ kJ ||w|/ Pdis,fsc
-1
25 25
15 15
st
1 st Compressor 1 Compressor
10 10
5 5
0 0 3 3
4 4
5 5
6 6
7
8 8
7 Pdis,fsc / MPa Pdis,fsc / MPa
9 9
10 10
Figure 11. Variations of 1st and 2nd specific compression work at various evaporator inlet Figure 11. of 1st compression work at various temperatures. 11.Variations Variations of and 1st 2nd andspecific 2nd specific compression work evaporator at variousinlet evaporator inlet temperatures. temperatures.
S S
0.4 0.4 0.2 0.2 0.0 0.0 -0.2 -0.2 -0.4 -0.4 -0.6 -0.6 -0.8 -0.8
Tout,gc= 35℃ T ,gc= 35℃ Tinout = −26.1℃ ,evap T = −26.1℃ Pinin,gc,evap = 10 MPa Pin,gc= 10 MPa
Tout,ic=35℃ Tout,ic=35℃ Tout =40℃ ,ic Tout,ic=40℃ Tout,ic=50℃ Tout,ic=50℃
1.95 1.95
COP Maximum COP Maximum
1.90 1.90 1.85 1.85 1.80 1.80 1.75 1.75 1.70 1.70
3.5 3.5
4.0 4.0
4.5 4.5
5.0 5.0
5.5 5.5
6.0 6.0
6.5
7.0
7.0 P6.5 / MPa dis,fsc Pdis,fsc / MPa
7.5 7.5
8.0 8.0
8.5 8.5
9.0 9.0
9.5 9.5
10.0 10.0
Figure Figure12. 12.Sensitivity Sensitivityof ofCOP COPto tointer-stage inter-stage pressure pressure at at various various intercooler intercooler outlet outlet temperatures. temperatures. Figure 12. Sensitivity of COP to inter-stage pressure at various intercooler outlet temperatures.
As shown As shown in in Figure Figure 12, 12, the thesudden suddenchange changein inthe thesensitivity sensitivityweakens weakensgradually graduallyas asthe theintercooler intercooler As shown in Figure 12, the sudden change in the sensitivity weakens gradually as the intercooler outlet temperature increases and disappears completely after the intercooler outlet temperature outlet increases and disappears completely after the intercooler outlet temperature outlet temperature temperature increases and disappears completely after the intercooleraffects outlet not temperature reaches about 50 °C. is also found that the intercooler outlet temperature only the ◦ C. It reaches about 50 It is also found that the intercooler outlet temperature affects not only reaches about 50 °C. It is also found that the intercooler outlet temperature affects not only the the amplitude of this sudden change but also its position. As the intercooler outlet temperature increases amplitude of this sudden change but also its position. As the intercooler outlet temperature increases amplitude of 40 this sudden change but also itsfor position. As the intercooler outlet temperature increases from 35 °C ◦ Cto ◦ C,the from 35 to 40 40°C, theinter-stage inter-stagepressure pressure for forthe thesudden suddenchange changein inthe thesensitivity sensitivityto tooccur occurincreases increases from 35 °C to °C, the inter-stage pressure the sudden change in the sensitivity to occur increases from 8 MPa MPatoto8.8 8.8MPa, MPa, which should be attributed tosteep the steep change rate of the second-stage from 8 which should be attributed to the change rate of the second-stage specific from 8 compression MPa to 8.8 MPa, which should be attributed to the steep change rate of the second-stage specific work at the corresponding pressures, as shown in Figure 13. compression work at work the corresponding pressures, as shownasinshown Figurein13. specific compression at the corresponding pressures, Figure 13.
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16 of 20 15 15 of of 19 19
25 25
TTout,ic== 35 35℃ ℃ out,ic TTout,ic== 40 ℃ 40℃ out,ic
20 20
-1
kg-1 MPa MPa-1 w|/PPdis,fsc/ /kJ kJkg ||w|/ dis,fsc
-1
TTout,ic== 50 50℃ ℃ out,ic TTin,evap== −−26.1 26.1℃ ℃ in,evap TTout,gc== 35 35℃ ℃
15 15
nd
22nd
out,gc
PPin,gc=10 =10 MPa MPa in,gc
⬧⬧ ⬧⬧
10 10 st
11st Compressor Compressor 55
00 44
55
66
77
88
99
10 10
PPdis,fsc // MPa MPa dis,fsc
Figure 13. Variations Variations 1st of 1st and 2nd specific compression works at various intercooler Figure Figure 13. 13. Variations of of 1st and and 2nd 2nd specific specific compression compression works works at at various various intercooler intercooler outlet outlet outlet temperatures. temperatures. temperatures. 0.4 0.4 0.2 0.2 0.0 0.0
SS
-0.2 -0.2
TTout,gc=30 =30℃ ℃ out,gc
TTout,ic== 35 35℃ ℃ out,ic TTin,evap== −−26.1 26.1℃ ℃
TTout,gc=35 =35℃ ℃ out,gc
PPin,gc== 10 10 MPa MPa in,gc
TTout,gc=33 =33℃ ℃ out,gc
-0.4 -0.4 -0.6 -0.6 -0.8 -0.8
in,evap
2.10 2.10 2.05 2.05
COP MaximumCOP Maximum
2.00 2.00 1.95 1.95 1.90 1.90 1.85 1.85 1.80 1.80 1.75 1.75 1.70 1.70
3.5 3.5
4.0 4.0
4.5 4.5
5.0 5.0
5.5 5.5
6.0 6.0
6.5 6.5
7.0 7.0
7.5 7.5
8.0 8.0
8.5 8.5
9.0 9.0
9.5 9.5
10.0 10.0
PPdis,fsc // MPa MPa dis,fsc
Figure 14. Sensitivity of COP to inter-stage pressure at various gas cooler temperatures. Figure cooler outlet outlet Figure 14. 14. Sensitivity Sensitivity of of COP COP to to inter-stage inter-stage pressure pressure at at various various gas gas cooler outlet temperatures. temperatures.
From From Figure Figure 14, 14, itit can can be be seen seen that that the the gas gas cooler cooler outlet outlet temperature temperature has has no no effect effect on on the the From of Figure 14, it can be seen that the gas cooler outlet temperature has no effect on the sensitivity sensitivity maximum COP to the inter-stage pressure, which can be explained by the fact that sensitivity of maximum COP to the inter-stage pressure, which can be explained by the fact that the the of maximumgas COP to the inter-stage pressure, which can be explained by the fact thathas the variation in variation variation in in gas cooler cooler outlet outlet temperature temperature just just affects affects the the capacity capacity of of evaporator evaporator but but has no no influence influence gas cooler outlet temperature just affects the capacity of evaporator but has no influence on the firston on the the firstfirst- and and second-stage second-stage compression compression power, power, as as shown shown in in Figure Figure 15. 15. and second-stage compression power, as shown in Figure 15.little effect on the position of the sudden As shown in Figure 16, the gas cooler inlet pressure has As shown in Figure 16, the gas cooler inlet pressure has little effect on the position of the sudden As shown in Figure 16, the gas cooler inlet pressure has little effect on the Itposition of the sudden change change of of the the sensitivity, sensitivity, but but can can affect affect the the amplitude amplitude of of the the sudden sudden change. change. It can can be be explained explained by by change of the sensitivity, but can affect the amplitude of the sudden change. It can be explained by the the fact that the abrupt change of the second-stage compression power becomes smaller with an the fact that the abrupt change of the second-stage compression power becomes smaller with an increase increase in in the the gas gas cooler cooler inlet inlet pressure, pressure, which which is is shown shown in in Figure Figure 17. 17.
Energies 2018, 11, 1279
17 of 20
fact that the abrupt change of the second-stage compression power becomes smaller with an increase in the gas inlet pressure, Energies 2018,cooler 11,xxFOR FOR PEER REVIEWwhich is shown in Figure 17. 16 of of 19 19 Energies 2018, 11, PEER REVIEW 16 25 25
30℃ ℃ TTout == 30 out,gc ,gc 33℃ ℃ TTout == 33 out,gc ,gc 35℃ ℃ TTout == 35 out,gc ,gc
-1
-1
-1 -1 // kJ || kg MPa kJ kg MPa w|/ w|/ P Pdis,fsc dis,fsc
20 20
26.1℃ ℃ TTinin,evap == −−26.1 ,evap 35℃ ℃ TTout == 35 out,ic ,ic
15 15
nd nd
Compressor 22 Compressor
=10 MPa MPa PPinin,gc,gc=10 10 10 stst
Compressor 11 Compressor 55
00 44
55
66
77
88
99
10 10
MPa PPdisdis,fsc //MPa ,fsc
Figure 15. Variations of specific compression at various gas outlet cooler 15. Variations Variations of 1st 1st 1st andand 2nd 2nd specific compression work work at various various gas cooler cooler outlet Figure of and 2nd specific compression work at gas outlet temperatures. temperatures. temperatures. 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0
S S
-0.2 -0.2
=9MPa MPa PPinin,gc,gc=9
-0.4 -0.4 -0.6 -0.6
=10MPa MPa PPinin,gc,gc=10
-0.8 -0.8
=12MPa MPa PPinin,gc,gc=12
=Tout,gc==35 35℃ ℃ TTout =T out,ic,ic out ,gc 26.1℃ ℃ TTinin,evap ==−−26.1 ,evap
-1.0 -1.0 1.95 1.95
Maximum COP Maximum COP
1.90 1.90 1.85 1.85 1.80 1.80 1.75 1.75 1.70 1.70 1.65 1.65 1.60 1.60 3.5 3.5
4.0 4.0
4.5 4.5
5.0 5.0
5.5 5.5
6.0 6.0
6.5 6.5
7.0 7.0
7.5 7.5
8.0 8.0
8.5 8.5
9.0 9.0
9.5 9.5
10.0 10.0
MPa PPdisdis,fsc //MPa ,fsc
Figure 16. 16. Sensitivity Sensitivity of of COP COP to tointer-stage inter-stage pressure pressure at pressures. Figure at various various gas gas cooler cooler inlet inlet pressures. pressures.
Energies 2018, 11, 1279 Energies 2018, 11, x FOR PEER REVIEW
18 of 20 17 of 19
25
Pin,gc= 9 MPa Pin,gc= 10 MPa Pin,gc= 12 MPa
20
-1
|w|/Pdis,fsc / kJ kg MPa
-1
Tin,evap= −26.1℃ Tout,ic=Tout,gc= 35℃
15
10 st
1 Compressor 5 nd
2 Compressor 0 4
5
6
7
8
9
10
Pdis,fsc / MPa
Figure 17. Variations of 1st and 2nd 2nd specific specific compression compression work work at at various various gas gas cooler cooler inlet inletpressures. pressures.
5. Conclusions 5. Sensitivity analysis analysis of of the the operating operating parameters parameters in in three three typical typical expander-based expander-basedtranscritical transcriticalCO CO22 Sensitivity refrigeration cycles cycles was was conducted, conducted, and and the the calculated calculated results results were were discussed. discussed. Some Some conclusions conclusions can can refrigeration be drawn drawn as as follows: follows: be (a) The cooler outlet, outlet, (a) The parameters, parameters, i.e., i.e., the the inlet inlet pressure pressure of of gas gas cooler, cooler, the the temperatures temperatures at at gas gas cooler evaporator inletand andintercooler intercooleroutlet outlet should monitored controlled in turn, owing to evaporator inlet should be be monitored andand controlled in turn, owing to their their significant influences on the maximum COP. significant influences on the maximum COP. (b) It better to control the the gas gas cooler cooler inlet zone higher higher than than the the optimal optimal pressure, (b) It is is better to control inlet pressure pressure in in aa zone pressure, based on the great difference in the sensitivity of maximum COP to the pressure at the the gas gas cooler cooler based on the great difference in the sensitivity of maximum COP to the pressure at inlet before and after the optimum value. This measure can reduce the control precision without inlet before and after the optimum value. This measure can reduce the control precision without an an excessive excessive loss loss of of system system performance. performance. (c) The lower the outlet needed, (c) The lower the outlet temperature temperature of of gas gas cooler cooler drops, drops, the the higher higher its its control control precision precision is is needed, especially in the case of high evaporation temperature. especially in the case of high evaporation temperature. (d) Compared to the refrigeration field, the mentioned CO2 cycles used in the area of air(d) Compared to the refrigeration field, the mentioned CO2 cycles used in the area of air-conditioning conditioning should be as far as possible to increase the evaporation temperature, because the should be as far as possible to increase the evaporation temperature, because the sensitivity sensitivity increased significantly when the evaporation temperature is higher than 5 °C. increased significantly when the evaporation temperature is higher than 5 ◦ C. (e) When the intercooler outlet temperature exceeds 45 ◦°C or the proposed two-stage CO2 cycles are (e) When the intercooler outlet temperature exceeds 45 C or the proposed two-stage CO2 cycles are used in the refrigeration field (e.g., the evaporator temperature of −26 ◦°C), the control accuracy used in the refrigeration field (e.g., the evaporator temperature of −26 C), the control accuracy can be reduced. can be reduced. (f) In TEADFC cycle, there may be dual peaks of the maximum COP when the inter-stage pressure (f) In TEADFC cycle, there may be dual peaks of the maximum COP when the inter-stage pressure is around 8 MPa, which may cause a PI-controlled CO2 system to deviate from the optimal value. is around 8 MPa, which may cause a PI-controlled CO2 system to deviate from the optimal value. But the dual peaks completely disappear when the intercooler outlet temperature exceeds 50 °C. But the dual peaks completely disappear when the intercooler outlet temperature exceeds 50 ◦ C. Author Contributions: B.Z., M.W. and X.Z. built the mathematical model; B.Z., C.J. and L.C. processed the calculated data; B.Z. andB.Z., L.L. M.W. wrote and the paper. K.-I.S. the article. Author Contributions: X.Z. built thepolished mathematical model; B.Z., C.J. and L.C. processed the calculated data; B.Z. and L.L. wrote the paper. K.-I.S. polished the article. Acknowledgments: This research was supported by the National Natural Science Foundation of China (Nos. Acknowledgments: This research was supported the National Natural Science Foundation 51504182, 51674188, 51404191, 51405381), the Naturalby Science Basic Research Plan of Shaanxi Provinceof of China China (Nos. 51504182, 51674188, 51404191, 51405381), the Natural Science Basic Research Plan of Shaanxi Province (No. 2015JQ5187), the Scientific Research Program funded by the Shaanxi Provincial Education Department (No. of China (No. 2015JQ5187), the Scientific Research Program funded by the Shaanxi Provincial Education 15JK1466), the Project funded by China Postdoctoral Science Foundation (No. 2015M582685), and Outstanding Youth Science Fund of Xi’an University of Science and Technology (No. 2018YQ2-01). This research was also
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Department (No. 15JK1466), the Project funded by China Postdoctoral Science Foundation (No. 2015M582685), and Outstanding Youth Science Fund of Xi’an University of Science and Technology (No. 2018YQ2-01). This research was also supported by the National Research Council of Science & Technology (NST) grant by the Korea government (MSIP) (No. CRC-16- 38502-KICT). Conflicts of Interest: The authors declare no conflict of interest.
Nomenclature COP Cp H P q S T w Greek symbols η Subscript c e ev dis fsc gc ic in is loss out ssc Abbreviation SE TEDSC TEADFC
coefficient of performance isobaric specific heat, kJ/kg·K specific enthalpy, kJ/kg pressure, MPa cooling capacity, kJ/kg sensitivity temperature, ◦ C specific compression work, kJ/kg efficiency compressor expander evaporator discharge first-stage compressor gas cooler intercooler inlet isentropic loss outlet second-stage compressor Single-stage compression with an expander Two-stage compression with an intercooler and an expander driving the second-stage compressor Two-stage compression with an intercooler and an expander assisting in driving the first-stage compressor
References 1. 2. 3. 4. 5. 6. 7. 8.
Lorentzen, G. The use of natural refrigerants: A complete solution to the CFC/HCFC predicament. Int. J. Refrig. 1995, 18, 190–197. [CrossRef] Lorentzen, G. Revival of carbon dioxide as a refrigerant. Int. J. Refrig. 1994, 17, 292–301. [CrossRef] Lorentzen, G.; Pettersen, J. A new, efficient and environmentally benign system for car air conditioning. Int. J. Refrig. 1993, 16, 4–12. [CrossRef] Robinson, D.M.; Groll, E.A. Efficiencies of transcritical CO2 cycles with and without an expansion turbine. Int. J. Refrig. 1998, 21, 577–589. [CrossRef] Yang, J.L.; Ma, Y.T.; Li, M.X.; Guan, H.Q. Exergy analysis of transcritical carbon dioxide refrigeration cycle with an expander. Energy 2005, 30, 1162–1175. [CrossRef] Yang, J.L.; Ma, Y.T.; Liu, S.C. Performance investigation of transcritical carbon dioxide two-stage compression cycle with expander. Energy 2007, 32, 237–245. [CrossRef] Cho, H.Y.; Lee, M.Y.; Kim, Y.C. Numerical evaluation on the performance of advanced CO2 cycles in the cooling mode operation. Appl. Therm. Eng. 2009, 29, 1485–1492. [CrossRef] Nickl, J.; Will, G.; Quack, H.; Kraus, W.E. Integration of a three-stage expander into a CO2 refrigeration system. Int. J. Refrig. 2005, 28, 1219–1224. [CrossRef]
Energies 2018, 11, 1279
9. 10.
11. 12. 13.
14. 15. 16. 17. 18. 19.
20. 21. 22. 23. 24.
20 of 20
Zhang, B.; Peng, X.Y.; He, Z.L.; Xing, Z.W.; Shu, P.C. Development of a double acting free piston expander for power recovery in transcritical CO2 cycle. Appl. Therm. Eng. 2007, 27, 1629–1636. [CrossRef] Huff, H.J.; Radermacher, R. Experimental investigation of a scroll expander in a carbon dioxide air-conditioning system. In Proceedings of the 21st IIR International Congress of Refrigeration, ICR0485, Washington, DC, USA, 17–22 August 2003. Zha, S.T. Study and Development of CO2 Transcritical Expander. Ph.D. Thesis, University of Tianjin, Tianjin, China, 2002. (In Chinese) Hu, J.; Li, M.; Zhao, L.; Xia, B.; Ma, Y. Improvement and experimental research of CO2 two-rolling piston expander. Energy 2015, 93, 2199–2207. [CrossRef] Fukuta, M.; Yanagisawa, T.; Radermacher, R. Performance prediction of vane type expander for CO2 cycle. In Proceedings of the 21st IIR International Congress of Refrigeration, ICR0251, Washington, DC, USA, 17–22 August 2003. Jia, X.; Zhang, B.; Pu, L.; Guo, B.; Peng, X. Improved rotary vane expander for trans-critical CO2 cycle by introducing high-pressure gas into the vane slots. Int. J. Refrig. 2011, 34, 732–741. [CrossRef] Baek, J.S.; Groll, E.A.; Lawless, P.B. Piston-cylinder work producing expansion device in a transcritical carbon dioxide cycle. Part I: Experimental investigation. Int. J. Refrig. 2005, 28, 141–151. [CrossRef] Baek, J.S.; Groll, E.A.; Lawless, P.B. Piston-cylinder work producing expansion device in a transcritical carbon dioxide cycle. Part II: Theoretical model. Int. J. Refrig. 2005, 28, 152–164. [CrossRef] Ferrara, G.; Ferrari, L.; Fiaschi, D.; Galoppi, G.; Karellas, S.; Secchi, R.; Tempesti, D. Energy recovery by means of a radial piston expander in a CO2 refrigeration system. Int. J. Refrig. 2016, 72, 147–155. [CrossRef] Peñarrocha, I.; Llopis, R.; Tárrega, L.; Sánchez, D.; Cabello, R. A new approach to optimize the energy efficiency of CO2 transcritical refrigeration plants. Appl. Therm. Eng. 2014, 67, 137–146. [CrossRef] Cecchinato, L.; Chiarello, M.; Corradi, M.; Fornasieri, E.; Minetto, S.; Stringari, P.; Zilio, C. Thermodynamic analysis of different two-stage transcritical carbon dioxide cycles. Int. J. Refrig. 2009, 32, 1058–1067. [CrossRef] Srinivasan, K.; Sheahen, P.; Sarathy, C.S.P. Optimum thermodynamic conditions for upper pressure limits of transcritical carbon dioxide refrigeration cycle. Int. J. Refrig. 2010, 33, 1395–1401. [CrossRef] Cavallini, A.; Cecchinato, L.; Corradi, M.; Fornasieri, E.; Zilio, C. Two-stage transcritical carbon dioxide cycle optimizations: A theoretical and experimental analysis. Int. J. Refrig. 2005, 28, 1274–1283. [CrossRef] Luo, J. System Sensitivity Theory, 1st ed.; Northwest Polytechnical University Press: Xi’an, China, 1990; p. 22. ISBN 7-5612-0179-6/TP.32. (In Chinese) Lemmon, E.W.; Huber, M.L.; Mclinden, M.O. NIST Standard Reference Database 23; Version 9.0; NIST: Gaithersburg, MD, USA, 2010. Klein, S.; Alvarado, F. Engineering Equation Solver; Academic Version 8.400; F-Chart Software: Middleton, WI, USA, 2009. © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
