Optimization and Comparison of Two Combined Cycles Consisting of CO 2 and Organic Trans-Critical Cycle for Waste Heat Recovery

: CO 2 -based trans-critical and supercritical cycles have received more and more attention for power generation in many applications such as solar and nuclear energy due to the desirable thermal stability and properties of CO 2 and the high e ﬃ ciency and compact size of the plant. In this study, two combined cycles driven by the ﬂue gas exhausted from the LM2500 + gas turbine, CO 2 -TC + OTC (organic trans-critical cycle) and CO 2 -TC / OTC, which can achieve a good trade-o ﬀ between thermal e ﬃ ciency and utilization of the waste heat, are investigated. Parameters optimization is carried out by means of genetic algorithm to maximize the net power output of the combined cycle and the e ﬀ ects of the key parameters on the cycle performance are examined. Results show that the exergy e ﬃ ciency of CO 2 -TC + OTC is about 2% higher than that of CO 2 -TC / OTC. In CO 2 -TC + OTC, the recuperation process of CO 2 causes the largest exergy loss; in CO 2 -TC / OTC, the largest exergy loss occurs in the heat recovery vapor generator, followed by the intermediate heat exchanger due to the larger variation of the speciﬁc heat capacity of CO 2 and organic ﬂuid in the heat addition process.


Introduction
Recovering waste heat from the engines, gas turbines and industrial processes such as cement, glass and metallurgy and so forth, can effectively improve energy utilization efficiency, thus reducing fossil fuel consumption and CO 2 emissions. In addition to the direct heat utilization of waste heat, such as preheating air and raw materials, building heating and so forth, power recovery is another practical option, especially for the medium-to-high temperature waste heat sources.
Organic Rankine cycle (ORC) and organic trans-critical cycle (OTC) prove to be the promising technologies for the heat to power conversion under the low-to-medium temperature heat sources [1], which is mainly attributed to the lower critical temperature and the dry or isentropic characteristics of the organic working fluids. However, the organic compounds will suffer thermal decomposition at relatively high temperature, which affects the performance of ORC and OTC under the medium-to-high heat source conditions. Thus, carbon dioxide (CO 2 ) has attracted more and more attention due to its high thermal stability. Additionally, it is environmentally friendly, non-corrosive, non-toxic, non-flammable, easy to obtain and with the desirable heat and mass transfer properties.
As the critical temperature of CO 2 is relatively low (30.98 • C), trans-critical cycle (TC) and supercritical cycle (SC) with CO 2 as the working fluid are commonly considered for the waste heat recovery. The CO 2 -TC features that the pressure of the heat addition process is higher than the critical pressure of CO 2 , while the heat rejection pressure is lower than the critical pressure. Both the pressures pressures of heat addition and heat rejection process of CO2-SC are above the critical pressure of CO2. Unlike the general Brayton cycle, the CO2 at the compressor inlet of CO2-SC is near the critical point, which is mainly to reduce the power consumption of the compression process since CO2 behaves more like an incompressible fluid in this region. A better temperature match between the flue gas and the supercritical CO2 can be achieved in the CO2-TC and CO2-SC, which enables the smaller exergy loss in the heat addition process of CO2 and higher utilization efficiency of the waste heat. In addition, the higher fluid density of supercritical CO2 and the lower volume ratio in the expansion process permits the efficient and compact turbomachinery design.
The critical pressure of CO2 is 7.38 MPa. Considering the conventional cooling water condition, the heat rejection pressure of CO2-TC is just slightly lower than the critical pressure [2]. Therefore, the pressure ratio of CO2-TC and CO2-SC is limited since the high pressure may threaten the safety of the system. The lower pressure ratio results in a lower temperature drop during the expansion process, which is detrimental to the thermal efficiency of the cycle. In this context, introducing a recuperator to recover the heat of turbine exhaust is an efficient solution to improve the cycle thermal efficiency. Echogen Power System LLC has developed the waste heat power system scalable from 250 kW to greater than 50 MW using the CO2-SC technology and they proved that the recuperative CO2-SC can provide the higher power output with the lower levelized cost of energy (LCOE) than the conventional steam Rankine cycle for the waste heat recovery of gas turbine [3].
In a recuperator, the cold side is the high pressure supercritical fluid and the hot side is the lowpressure vapor (for CO2-TC) or supercritical fluid (for CO2-SC). The specific heat capacity of the CO2 on both sides is quite different, especially in the low-temperature region (see Figure 1a), which leads to the lower recuperator effectiveness and larger exergy loss in the heat transfer process, as the T-Q diagram shows in Figure 1b. To compensate the drawback, the recompressed recuperative cycle is proposed, in which the recuperation process is occurred in two heat exchangers-high temperature recuperator and low temperature recuperator. The temperature match can be improved by adjusting the mass flow ratio of the cold and hot fluid in the low-temperature recuperator. Thus, the recompressed recuperative cycle shows the highest thermal efficiency among different cycle configurations based on CO2-SC [4]. In some applications, the higher thermal efficiency is the design objective for the CO2-TC and CO2-SC, such as nuclear [5], coal-fired [6] and solar [7] power plants. However, when it comes to waste heat recovery, we pay more attention to maximizing the net power output of the system since the waste heat is generally discharged into the environment after releasing heat to the plant. The recuperation and recompression mentioned above can increase the heat absorption temperature of CO2, which will accordingly reduce the heat extraction from the waste heat source.
To achieve the deep utilization of the waste heat for CO2-TC and CO2-SC systems, integrating a bottom cycle X to absorb the residual heat of the heat source is an effective solution, forming the CO2- In some applications, the higher thermal efficiency is the design objective for the CO 2 -TC and CO 2 -SC, such as nuclear [5], coal-fired [6] and solar [7] power plants. However, when it comes to waste heat recovery, we pay more attention to maximizing the net power output of the system since the waste heat is generally discharged into the environment after releasing heat to the plant. The recuperation and recompression mentioned above can increase the heat absorption temperature of CO 2 , which will accordingly reduce the heat extraction from the waste heat source. To achieve the deep utilization of the waste heat for CO 2 -TC and CO 2 -SC systems, integrating a bottom cycle X to absorb the residual heat of the heat source is an effective solution, forming the CO 2 -TC(SC)+X combined cycle. The proposed bottom cycles include CO 2 -SC [8], CO 2 -TC [9] and ORC [10]. Another solution to ensure the higher utilization efficiency of the waste heat is to use a bottom cycle Y to recover the heat of turbine exhaust CO 2 instead of using the recuperator, forming the CO 2 -TC(SC)/Y combined cycle. Similarly, the bottom cycles can be CO 2 -TC [11], CO2-SC [12], ORC [13], OTC [14]. These researches have indicated that the two kinds of the combined cycle can achieve better thermodynamic performance than the stand-alone recuperated and recompressed CO 2 -TC and CO 2 -SC. It is worth mentioning that if the bottom cycle is the same as the top cycle, they can share some components, such as the cooler and compressor (for CO 2 -SC) or condenser and pump (for CO 2 -TC), so as to reduce the cost and space of the combined system. Correspondingly, the endothermic pressure and exothermic pressure of the top and bottom cycles must be kept equal respectively, which may lead to the insufficient optimization of the system performance.
Reference [15] gave a thorough literature review and detailed analysis of different layouts of CO 2 -SC. However, the research of a clear comparison between the above two kinds of the combined cycle is quite rare. In this study, CO 2 -TC is selected as the top cycle and OTC is selected as the bottom cycle owes to its better temperature match with the waste heat source, forming two combined cycles: CO 2 -TC+OTC, CO 2 -TC/OTC. The purpose of this study is to find out which of the two combined cycles shows better thermodynamic performance for waste heat recovery. The influence of some key parameters on the system performance is also examined. The parametric optimization is performed to maximize the net power output of the two combined cycles by using genetic algorithm based on the MATLAB platform and the control parameters in genetic algorithm (GA) have been described in our previous work [16]. Pentane and R134a are selected as the working fluid for OTC and the thermodynamic properties of the fluids are calculated by the Refprop NIST 9.0 [17]. The waste heat source to drive the combined cycles is from the LM2500+ gas turbine [18] and the initial temperature and mass flow rate of the exhaust gas are 533.8 • C and 89.5 kg/s.

CO 2 -TC+OTC
According to the results of Reference [10], the thermodynamic and economic performance of the combined cycle CO 2 -SC+ORC with regenerative CO 2 -SC as the top cycle is superior to that with recompressed CO 2 -SC. Hence, a single recuperated layout of CO 2 -TC is considered in this study.
The schematic and T-s diagrams of the regenerative CO 2 -TC+OTC combined system are shown in Figures 2 and 3. The exhaust gas releases heat to the CO 2 and organic fluid in HRVG1 and HRVG2 (heat recovery vapor generator) successively. The generated high temperature CO 2 and organic fluid expand in the turbine1 and turbine2 to do work (1H-2H, 1L-2L) respectively. The organic fluid exhausted from turbine2 flows into the condenser2 and releases heat to the cooling water (2L-4L). The saturated liquid leaving the condenser2 will be pressurized by the pump2 (4L-5L) and then enters the HRVG2 to absorb heat from the heat source (5L-1L). The exhaust CO 2 from turbine1 enters the recuperator to preheat the low-temperature CO 2 coming from the pump1 (2H-3H) and then liquefied by the cooling water in the condenser1 (3H-4H). The liquid CO 2 exiting condenser1 is compressed by the pump1 (4H-5H) and heated in the recuperator (5H-6H) before flowing into the HRVG1 to absorb the waste heat (6H-1H).

CO2-TC/OTC
The schematic and T-s diagrams of the CO2-TC/OTC combined system are shown in Figures 4 and 5. To extract as much heat as possible from the waste heat source, the recuperator is not included in the top CO2-TC, which means the CO2 stream at pump1 exit flows directly into the HRVG without preheating. The CO2 stream exhausted from turbine1 drives the bottom OTC system and the organic fluid is heated in the IHE (intermediate heat exchanger).

CO2-TC/OTC
The schematic and T-s diagrams of the CO2-TC/OTC combined system are shown in Figures 4 and 5. To extract as much heat as possible from the waste heat source, the recuperator is not included in the top CO2-TC, which means the CO2 stream at pump1 exit flows directly into the HRVG without preheating. The CO2 stream exhausted from turbine1 drives the bottom OTC system and the organic fluid is heated in the IHE (intermediate heat exchanger).

CO 2 -TC/OTC
The schematic and T-s diagrams of the CO 2 -TC/OTC combined system are shown in Figures 4 and 5. To extract as much heat as possible from the waste heat source, the recuperator is not included in the top CO 2 -TC, which means the CO 2 stream at pump1 exit flows directly into the HRVG without preheating. The CO 2 stream exhausted from turbine1 drives the bottom OTC system and the organic fluid is heated in the IHE (intermediate heat exchanger).

Thermodynamic Modeling
The following assumptions were made in establishing the thermodynamic models of the combined system. The working fluid was in a steady flow state in each component. The change in kinetic and potential energies of working fluid flowing in the system was negligible. The pressure drop and heat dissipation in the heat exchangers and pipes were also neglected. Table 1 gives the energy and exergy balance equations in each component of the two combined cycles. Wherein,  Q is the heat transferred in the process, kW;  m , h and s denote the mass flow rate, enthalpy and entropy of the fluid, kg/s, kJ/kg, kJ/(kgK); 0 T means the ambient temperature, K;  W refers to the power input or output of the process, kW;  I is the exergy loss of the process, kW. The equations in turbine1, condenser1, pump1, turbine2, condenser2, pump2 of CO2-TC/OTC are the same as that of the CO2-TC+OTC.

Thermodynamic Modeling
The following assumptions were made in establishing the thermodynamic models of the combined system. The working fluid was in a steady flow state in each component. The change in kinetic and potential energies of working fluid flowing in the system was negligible. The pressure drop and heat dissipation in the heat exchangers and pipes were also neglected. Table 1 gives the energy and exergy balance equations in each component of the two combined cycles. Wherein,  Q is the heat transferred in the process, kW;  m , h and s denote the mass flow rate, enthalpy and entropy of the fluid, kg/s, kJ/kg, kJ/(kgK); 0 T means the ambient temperature, K;  W refers to the power input or output of the process, kW;  I is the exergy loss of the process, kW. The equations in turbine1, condenser1, pump1, turbine2, condenser2, pump2 of CO2-TC/OTC are the same as that of the CO2-TC+OTC.

Thermodynamic Modeling
The following assumptions were made in establishing the thermodynamic models of the combined system. The working fluid was in a steady flow state in each component. The change in kinetic and potential energies of working fluid flowing in the system was negligible. The pressure drop and heat dissipation in the heat exchangers and pipes were also neglected. Table 1 gives the energy and exergy balance equations in each component of the two combined cycles. Wherein, .
Q is the heat transferred in the process, kW; . m, h and s denote the mass flow rate, enthalpy and entropy of the fluid, kg/s, kJ/kg, kJ/(kgK); T 0 means the ambient temperature, K; . W refers to the power input or output of the process, kW; . I is the exergy loss of the process, kW. The equations in turbine1, condenser1, pump1, turbine2, condenser2, pump2 of CO 2 -TC/OTC are the same as that of the CO 2 -TC+OTC. Table 1. Thermodynamic models in each component of the two combined cycles.

Component
Equations The net power output of the combined cycle is given by: The exergy efficiency of the combined cycle is defined as: where h g,0 and s g,0 are the enthalpy and entropy of exhaust gas when it is cooled to the ambient temperature.

Turbine Efficiency Calculation
A three-stage axial turbine was considered for the CO 2 -TC and OTC systems. The turbine efficiency varies with the operating parameters and thermophysical properties of the working fluid. Reference [19] indicated that the turbine efficiency can be evaluated based on three independent variables including the size parameter SP, volume ratio Vr and the specific speed Ns. The calculation correlation for the maximum efficiency of a three-stage axial turbine under the optimum specific speed Energies 2020, 13, 724 7 of 16 given in Reference [19] is shown as Equation (3) and the coefficients used in the correlation are listed in Table 2. (3)

Decision Variables and Specified Parameters
The decision variables in the optimization process of the combined cycle were the turbine inlet pressure and temperature for CO 2 -TC and OTC. The ranges of the variables are shown in Table 3. To ensure the safe and stable operation of the system, the maximum heat addition pressure of CO 2 and organic fluid as set as 25 MPa. In order to avoid liquid erosion of the turbine blades, the expansion process was not allowed to go through the saturated zone for the OTC system. T stable,limit refers to the maximum temperature at which the organic fluid does not decompose and the values of T stable,limit for pentane and R134a are 280 • C [20] and 368 • C [21] respectively. The specified parameters of the combined system are listed in Table 4. The composition and mass fraction of the exhaust gas were as follows: N 2 = 76%, H 2 O = 11%, CO 2 = 13%. The condensing temperature of both the CO 2 -TC and OTC was 25 • C. It should be noted that the pinch point temperature difference always occurs at the outlet of hot fluid in the recuperator (see Figure 1b); however, in the heat exchange process between the exhaust gas and CO 2 , the exhaust gas and organic fluid in HRVG, as well as between the CO 2 and organic fluid in IHE, the position of the pinch point temperature difference varies with the temperature and pressure of the fluids. Therefore, in the optimization process, the outlet temperatures of the hot fluid that is, T g,m , T g,out and T 3H were instantaneously adjusted to ensure that the pinch point temperature difference in the heat exchange process was 15 • C.

Performance Analysis of CO 2 -TC+OTC
The variations of the net power output of CO 2 -TC, OTC using R134a and combined cycle with the turbine inlet temperature of CO 2 (T 1H ) are shown in Figure 6. The heat addition pressure of CO 2 (P 1H ) remains at 20 MPa and the temperature of exhaust CO 2 (T 2H ) increases with the increase of T 1H . After the recuperation process, the HRVG inlet temperature of CO 2 (T 6H ) will rise accordingly, which results in the increase of thermal efficiency and the decrease of heat absorption of CO 2 -TC. Hence, under the combined effect of the two trends, the net power output of CO 2 -TC increases first and then decreases.
As the T g,m increases, the thermal efficiency and net power output of OTC increase. It should be noted that the net power output of OTC shown in Figure 6 is the maximum power under the heat source condition whose initial temperature is T g,m corresponding to different T 1H . The effects of turbine inlet temperature and pressure of the organic working fluid on the thermal efficiency and net power output of OTC have been illustrated in our previous work [16].
The increment of the net power output of OTC is greater than the decrement of the net power output of CO 2 -TC. Thus, the maximum total net power output of the combined cycle is achieved when the T 1H reaches its upper limit.

Performance Analysis of CO2-TC+OTC
The variations of the net power output of CO2-TC, OTC using R134a and combined cycle with the turbine inlet temperature of CO2 (T1H) are shown in Figure 6. The heat addition pressure of CO2 (P1H) remains at 20 MPa and the temperature of exhaust CO2 (T2H) increases with the increase of T1H. After the recuperation process, the HRVG inlet temperature of CO2 (T6H) will rise accordingly, which results in the increase of thermal efficiency and the decrease of heat absorption of CO2-TC. Hence, under the combined effect of the two trends, the net power output of CO2-TC increases first and then decreases.
As the Tg,m increases, the thermal efficiency and net power output of OTC increase. It should be noted that the net power output of OTC shown in Figure 6 is the maximum power under the heat source condition whose initial temperature is Tg,m corresponding to different T1H. The effects of turbine inlet temperature and pressure of the organic working fluid on the thermal efficiency and net power output of OTC have been illustrated in our previous work [16].
The increment of the net power output of OTC is greater than the decrement of the net power output of CO2-TC. Thus, the maximum total net power output of the combined cycle is achieved when the T1H reaches its upper limit.  The variations of net power output with the turbine inlet pressure of CO 2 (P 1H ) are shown in Figure 7. The T 1H is kept at the upper limit of 518.8 • C. The thermal efficiency and heat addition of CO 2 -TC increase with the increase of P 1H , which leads to an increase in the net power output of CO 2 -TC. The net power output of OTC decreases as the T g,m decreases, while its decrement is lower than the increment of the net power output of CO 2 -TC. Thus, the optimum P 1H to maximize the net power output of the combined cycle is 25 MPa.
Energies 2020, 13, x FOR PEER REVIEW 9 of 17 CO2-TC increase with the increase of P1H, which leads to an increase in the net power output of CO2-TC. The net power output of OTC decreases as the Tg,m decreases, while its decrement is lower than the increment of the net power output of CO2-TC. Thus, the optimum P1H to maximize the net power output of the combined cycle is 25 MPa. The decision variables of the combined cycle CO2-TC+OTC with R134a and pentane as the working fluid are optimized by using genetic algorithm. The variations of the net power output of the combined cycle with generation in the optimization process are shown in Figure 8. It can be seen that when the generation reaches about 50, the result tends to converge. The optimized variables and the maximum net power output of the combined cycle CO2-TC+OTC are listed in Table 5. As analyzed above, the optimal turbine inlet temperature and pressure of CO2 are their respective upper limits. The net power output of the bottom cycle OTC is approximately 40% of that of the top cycle CO2-TC and OTC using pentane achieves a slightly higher net power output than that using R134a. Figure 9 reveals the T-Q diagram of the exhaust gas and working fluid and it can be seen that the thermal matching better the heat source and working fluid is quite better for the CO2-TC+OTC combined cycle. The decision variables of the combined cycle CO 2 -TC+OTC with R134a and pentane as the working fluid are optimized by using genetic algorithm. The variations of the net power output of the combined cycle with generation in the optimization process are shown in Figure 8. It can be seen that when the generation reaches about 50, the result tends to converge.
Energies 2020, 13, x FOR PEER REVIEW 9 of 17 CO2-TC increase with the increase of P1H, which leads to an increase in the net power output of CO2-TC. The net power output of OTC decreases as the Tg,m decreases, while its decrement is lower than the increment of the net power output of CO2-TC. Thus, the optimum P1H to maximize the net power output of the combined cycle is 25 MPa. The decision variables of the combined cycle CO2-TC+OTC with R134a and pentane as the working fluid are optimized by using genetic algorithm. The variations of the net power output of the combined cycle with generation in the optimization process are shown in Figure 8. It can be seen that when the generation reaches about 50, the result tends to converge. The optimized variables and the maximum net power output of the combined cycle CO2-TC+OTC are listed in Table 5. As analyzed above, the optimal turbine inlet temperature and pressure of CO2 are their respective upper limits. The net power output of the bottom cycle OTC is approximately 40% of that of the top cycle CO2-TC and OTC using pentane achieves a slightly higher net power output than that using R134a. Figure 9 reveals the T-Q diagram of the exhaust gas and working fluid and it can be seen that the thermal matching better the heat source and working fluid is quite better for the CO2-TC+OTC combined cycle.  The optimized variables and the maximum net power output of the combined cycle CO 2 -TC+OTC are listed in Table 5. As analyzed above, the optimal turbine inlet temperature and pressure of CO 2 are their respective upper limits. The net power output of the bottom cycle OTC is approximately 40% of that of the top cycle CO 2 -TC and OTC using pentane achieves a slightly higher net power output than that using R134a. Figure 9 reveals the T-Q diagram of the exhaust gas and working fluid and it can be seen that the thermal matching better the heat source and working fluid is quite better for the CO 2 -TC+OTC combined cycle.   Figure 10 indicates the variations of the outlet temperature of the pump (T5H) and turbine (T2H) and thermal efficiency with the heat addition pressure of CO2 (P1H) for the top cycle CO2-TC. The higher P1H results in the higher T5H and the lower T2H. The former leads to the increase of exhaust gas outlet temperature, which means the reduction of heat release for the heat source, while the latter increases the cycle thermal efficiency. The detrimental effect of the heat absorption reduction on the net power output of the cycle is less than that of the beneficial effect of the thermal efficiency increase. Thus, the net power output of CO2-TC increases as the P1H increases, as shown in Figure 11. The maximum net power output of OTC with R134a as the working fluid will decrease with the decrease of T2H, yet its decrement is smaller than the net power output increment of CO2-TC. Hence, as illustrated in Figure 11, increasing the heat addition pressure of CO2 helps to increase the total net power output of the combined cycle CO2-TC/OTC.   Figure 10 indicates the variations of the outlet temperature of the pump (T 5H ) and turbine (T 2H ) and thermal efficiency with the heat addition pressure of CO 2 (P 1H ) for the top cycle CO 2 -TC. The higher P 1H results in the higher T 5H and the lower T 2H . The former leads to the increase of exhaust gas outlet temperature, which means the reduction of heat release for the heat source, while the latter increases the cycle thermal efficiency. The detrimental effect of the heat absorption reduction on the net power output of the cycle is less than that of the beneficial effect of the thermal efficiency increase. Thus, the net power output of CO 2 -TC increases as the P 1H increases, as shown in Figure 11. The maximum net power output of OTC with R134a as the working fluid will decrease with the decrease of T 2H , yet its decrement is smaller than the net power output increment of CO 2 -TC. Hence, as illustrated in Figure 11, increasing the heat addition pressure of CO 2 helps to increase the total net power output of the combined cycle CO 2 -TC/OTC.  The influence of the turbine inlet temperature of CO2 (T1H) on the system net power output is shown in Figure 12. The average heat absorption temperature and heat rejection temperature of CO2-TC increase with the increase of T1H, thus there exists an optimal T1H to maximize the thermal efficiency and net power output of CO2-TC since the heat input of the cycle remains unchanged. Although the mass flow rate of CO2 decreases as T1H increases, the maximum net power output of OTC still increases with the increase of T2H. Finally, the maximum total net power output of the combined cycle CO2-TC/OTC is obtained as T1H reaches the upper limit.  The influence of the turbine inlet temperature of CO2 (T1H) on the system net power output is shown in Figure 12. The average heat absorption temperature and heat rejection temperature of CO2-TC increase with the increase of T1H, thus there exists an optimal T1H to maximize the thermal efficiency and net power output of CO2-TC since the heat input of the cycle remains unchanged. Although the mass flow rate of CO2 decreases as T1H increases, the maximum net power output of OTC still increases with the increase of T2H. Finally, the maximum total net power output of the combined cycle CO2-TC/OTC is obtained as T1H reaches the upper limit. The influence of the turbine inlet temperature of CO 2 (T 1H ) on the system net power output is shown in Figure 12. The average heat absorption temperature and heat rejection temperature of CO 2 -TC increase with the increase of T 1H , thus there exists an optimal T 1H to maximize the thermal efficiency and net power output of CO 2 -TC since the heat input of the cycle remains unchanged. Although the mass flow rate of CO 2 decreases as T 1H increases, the maximum net power output of OTC still increases with the increase of T 2H . Finally, the maximum total net power output of the combined cycle CO 2 -TC/OTC is obtained as T 1H reaches the upper limit. Energies 2020, 13, x FOR PEER REVIEW 12 of 17  Table 5. Also, the optimal turbine inlet temperature and pressure of CO2 are their respective upper limits for CO2-TC/OTC. Figure 13 shows the comparison of the net power output of two combined cycles and it can be seen that the net power output of CO2-TC+OTC is slightly higher than that of CO2-TC/OTC. The net power output of OTC in CO2-TC/OTC is higher than that of the OTC in CO2-TC+OTC and the pentane still outperforms R134a since it can extract a little more heat from the exhausted CO2 with a lower thermal efficiency of the cycle, which have been revealed in the T-Q diagram of CO2 and organic fluid in the IHE shown in Figure 14.   Table 5. Also, the optimal turbine inlet temperature and pressure of CO 2 are their respective upper limits for CO 2 -TC/OTC. Figure 13 shows the comparison of the net power output of two combined cycles and it can be seen that the net power output of CO 2 -TC+OTC is slightly higher than that of CO 2 -TC/OTC. The net power output of OTC in CO 2 -TC/OTC is higher than that of the OTC in CO 2 -TC+OTC and the pentane still outperforms R134a since it can extract a little more heat from the exhausted CO 2 with a lower thermal efficiency of the cycle, which have been revealed in the T-Q diagram of CO 2 and organic fluid in the IHE shown in Figure 14.  Table 5. Also, the optimal turbine inlet temperature and pressure of CO2 are their respective upper limits for CO2-TC/OTC. Figure 13 shows the comparison of the net power output of two combined cycles and it can be seen that the net power output of CO2-TC+OTC is slightly higher than that of CO2-TC/OTC. The net power output of OTC in CO2-TC/OTC is higher than that of the OTC in CO2-TC+OTC and the pentane still outperforms R134a since it can extract a little more heat from the exhausted CO2 with a lower thermal efficiency of the cycle, which have been revealed in the T-Q diagram of CO2 and organic fluid in the IHE shown in Figure 14.

Exergy Analysis of the Two Combined Cycles
The exergy analysis to evaluate the exergy loss in each component of the two combined cycles is shown in Table 6. The input exergy of the cycle is equal to the net power output plus the total dissipated exergy in each component. For CO2-TC+OTC, the sum of input exergy of top and bottom cycle and the exergy contained in the discharged gas is the total exergy of the heat source. For CO2-TC/OTC, the input exergy of OTC is from the exhausted CO2 and the heat source exergy is equal to the sum of the input exergy of the top cycle and the discharged gas exergy.
The exergy efficiency of CO2-TC+OTC is about 2% higher than that of CO2-TC/OTC. The distribution of the exergy loss in each component for the two combined cycles using pentane is shown in Figure 15. In CO2-TC+OTC, the recuperation process causes the largest exergy loss, which is due to the large difference in specific heat capacity of the hot and cold fluids in the recuperator (see Figure  1). Recompression can effectively reduce the exergy loss in the recuperator and the Tg,m will increase accordingly, which may lead to an increase of exergy loss in the organic HRVG. In CO2-TC/OTC, the largest exergy loss occurs in HRVG, followed by IHE. The specific heat capacity of CO2 and organic fluid in the heat addition process changes markedly (see Figure 16), resulting in the poor thermal match between exhaust gas and CO2 in HRVG and between CO2 and organic fluid in IHE.

Exergy Analysis of the Two Combined Cycles
The exergy analysis to evaluate the exergy loss in each component of the two combined cycles is shown in Table 6. The input exergy of the cycle is equal to the net power output plus the total dissipated exergy in each component. For CO 2 -TC+OTC, the sum of input exergy of top and bottom cycle and the exergy contained in the discharged gas is the total exergy of the heat source. For CO 2 -TC/OTC, the input exergy of OTC is from the exhausted CO 2 and the heat source exergy is equal to the sum of the input exergy of the top cycle and the discharged gas exergy. The exergy efficiency of CO 2 -TC+OTC is about 2% higher than that of CO 2 -TC/OTC. The distribution of the exergy loss in each component for the two combined cycles using pentane is shown in Figure 15. In CO 2 -TC+OTC, the recuperation process causes the largest exergy loss, which is due to the large difference in specific heat capacity of the hot and cold fluids in the recuperator (see Figure 1). Recompression can effectively reduce the exergy loss in the recuperator and the T g,m will increase accordingly, which may lead to an increase of exergy loss in the organic HRVG. In CO 2 -TC/OTC, the largest exergy loss occurs in HRVG, followed by IHE. The specific heat capacity of CO 2 and organic fluid in the heat addition process changes markedly (see Figure 16), resulting in the poor thermal match between exhaust gas and CO 2 in HRVG and between CO 2 and organic fluid in IHE.

Conclusions
This study aims to compare the thermodynamic performance of two combined cycles that is, CO 2 -TC+OTC and CO 2 -TC/OTC, for waste heat recovery. Parameters optimization is performed by means of genetic algorithm to maximize the net power output of the cycle and exergy analysis is also examined to evaluate the exergy loss in each component. R134a and pentane are considered as the working fluid for the bottom OTC and the decision variables are turbine inlet temperature and pressure of CO 2 and organic fluid in the top and bottom cycle respectively. The main conclusions are briefly summarized below: (1) As the turbine inlet temperature and pressure of CO 2 increase, the total net power output of the combined cycle is increased, even though the net power output of the top or bottom cycle may decrease as a result. (2) The exergy efficiency of CO 2 -TC+OTC is about 2% higher than that of CO 2 -TC/OTC and pentane outperforms R134a in using as the working fluid for bottom OTC. (3) In CO 2 -TC+OTC, the recuperation process of CO 2 causes the largest exergy loss due to the large difference in specific heat capacity of the hot and cold fluids in the recuperator. In CO 2 -TC/OTC, the largest exergy loss occurs in HRVG, followed by IHE, which is attributed to the poor temperature match in the heat exchanger caused by the larger variation of specific heat capacity of CO 2 and organic fluid in the heat addition process.