Exergy analysis for combined regenerative Brayton and inverse Brayton cycles with regeneration after the inverse cycle

Abstract

Exergy analysis and optimization is carried out for combined regenerative Brayton and inverse Brayton cycles with regenerator after the inverse cycle. The analytical formulae of exergy efficiency of the combined cycle and exergy losses of each component are derived. The largest exergy loss location is determined. It is shown that exergy efficiency increases with the increase in the effectiveness of regenerator in the critical range of the compressor pressure ratio of the bottom cycle. Furthermore, the exergy loss of combustion chamber is the largest in the combined cycle.

Headnote

Abstract

Exergy analysis and optimization is carried out for combined regenerative Brayton and inverse Brayton cycles with regenerator after the inverse cycle. The analytical formulae of exergy efficiency of the combined cycle and exergy losses of each component are derived. The largest exergy loss location is determined. It is shown that exergy efficiency increases with the increase in the effectiveness of regenerator in the critical range of the compressor pressure ratio of the bottom cycle. Furthermore, the exergy loss of combustion chamber is the largest in the combined cycle.

Copyright © 2016 International Energy and Environment Foundation - All rights reserved.

Keywords: Regenerative Brayton cycle; Inverse Brayton cycle; Combined cycle; Exergy analysis; Exergy efficiency; Exergy loss; Optimization.

(ProQuest: ... denotes formulae omitted.)

1. Introduction

As the industrial revolution happened after the second half of the twentieth century, the increasing utilization of the new technological products in our daily life caused more consumption of energy. In this situation, people want to construct new power and energy plants which could gain more efficiency from energy sector.

For the improvements of the energy systems, there are two basic methods including energy analysis and exergy analysis. The exergy analysis method [1-14] provides a more accurate measurement of the system efficiency than the energy analysis and determines the exergy loss location of the energy systems.

Steam and gas turbine combined cycles are considered as the most effective power plants whose application is becoming more and more common in mid and large scale power production [15]. The thermal efficiency of these cycle types exceeded 55 percent several years ago and is now at approximately 60 percent. In order to increase the power output, Braysson cycle (a hybrid gas turbine cycle) was proposed based on a conventional Brayton cycle for the high temperature heat addition process and an Ericsson cycle for the low temperature heat rejection process, and the energy analysis of the Braysson cycle was performed by Frost et al. [16] in 1997. Furthermore, the exergy analysis of the Braysson cycle was carried out by Zheng et al. [17] in 2001. Fujii et al. [18] studied a combined-cycle which composed with a top cycle (Brayton cycle) and a bottom cycle consisting of an expander followed by an inter-cooled compressor in 2001. It was found that when fixed the bottom cycle pressure ratio to 0.25 bar could avoid a rapid increase in gas flow axial velocity effectively. The use of two parallel inverse Brayton cycles instead of one was proposed in order to reduce the size of the overall power plant. Bianchi et al. [19] studied a combined-cycle consisting of a top cycle (Brayton cycle) and a bottom cycle (an inverse Brayton cycle in which air is compressed to atmospheric pressure) in 2002. Agnew et al. [20] proposed combined Brayton and inverse Brayton cycles in 2003, and performed the energy analysis of the combined cycle. It was found that the optimal expansion pressure of the inverse Brayton cycle is 0.5 bar for the optimum performance. Zhang et al. [21] performed the exergy analysis and optimization of the combined Brayton and inverse Brayton cycles in 2007. They found that exergy loss of combustion is the biggest in the cycle and followed by heat exchanger. Based on the combined Brayton and inverse Brayton cycles, Alabdoadaim et al. [22] proposed its developed configurations including regenerative cycle and reheat cycle, and they found that the use of regenerative Brayton cycle as top cycle can obtain higher thermal efficiency than the base cycle but with smaller work output based on energy analysis. Zhang et al. [23] performed the exergy analysis and optimization of the combined regenerative Brayton and inverse Brayton cycles with regeneration before the inverse cycle. Compared with combined regenerative Brayton and inverse Brayton cycles with regeneration before the inverse cycle proposed in Ref. [22], Zhang et al. [24] proposed a new combined cycle configuration with regeneration after the inverse cycle in order to keep work output of the combined cycle and studied the performance of the new combined cycle based on energy analysis.

In this paper, the exergy analysis for combined regenerative Brayton and inverse Brayton cycles with regeneration after the inverse cycle [24] will be performed. The purposes of the study are to determine the largest exergy loss location and optimize the exergy efficiency of the combined cycle by adjusting pressure ratio of the compressor of the regenerative Brayton cycle.

2. Cycle model

The proposed system in Ref. [24] is shown in Figure 1. It is constructed from a top regenerative Brayton cycle and a bottom inverse Brayton cycle. The top cycle is used as a gas generator to power the bottom cycles. The purpose of the turbine in the top cycle is solely to power the compressor. The power output of the combined cycle is totally produced by the bottom cycle. The energy performance analysis of the system was studied in Ref. [24]. Figure 2 shows T-s diagrams of the system. Process 1-2 is an irreversible adiabatic compression process in the compressor 1. Process 2-3 is an absorbed heat process in the regenerator. Process 3-4 is an absorbed heat process in the chamber. Process 4-5 is an irreversible adiabatic expansion process in the turbine 1. Process 5-6 is an irreversible adiabatic expansion process in the turbine 2. Process 6-7 is an evolved heat process in the regenerator. Process 7-8 is an evolved heat process in the heat exchanger. Process 8-9 is an irreversible adiabatic compression process in the compressor 2.

3. Exergy analysis and optimization

The following assumptions are made for simplicity and manipulating analytical expressions: The working fluid has constant specific heat ratio k ( k = cP / cV = 1.4 ). The mass flow rate m?? is fixed as 1 kg/s.

For the system operating in a steady state, the general exergy balance equation is given in Refs. [3-9]. After making an exergy balance equation, the expression of the exergy balance equation can be obtained for each component, respectively.

For the compressor 1, the following expression can be obtained:

... (1)

where c1 p 1 c1 c1 w = c Tψ η is specific work consumed of the compressor 1, p c is constant-pressure specific heat, T is temperature, 1 1 m 1 c c ψ =[straight phi] - , m = (k -1) k , c1 2 1 [straight phi] = P P is pressure ratio of compressor 1, P is pressure, e is exergy, 1 c η is the efficiency of the compressor 1, and ( ) . 1 1 1 1 1 In 1 In D c p c c c e = c T ?? +ψ η -m [straight phi] ?? is exergy loss of the compressor 1.

For the turbine 1, the following expression can be obtained:

... (2)

where t1 p 1 1 t1 t1 w = c Tτ ψ η is specific work output of the turbine 1, 1 1 1 1 m t t ψ = - [straight phi] , t1 4 5 [straight phi] = P P is pressure ratio of turbine 1, ( ) ( ) . 1 1 1 1 1 In 1 In 1/ D t P t t t e = c T ?? -η ψ -m [straight phi] ?? is exergy loss of turbine 1, and 1t η is efficiency of the turbine 1.

For the turbine 2, the following expression can be obtained:

... (3)

where ( ) t 2 p 1 t 2 t 2 1 c1 c1 w = c Tη ψ τ -ψ η is specific work output of the turbine 2, 2 2 1 1 m t t ψ = - [straight phi] , t 2 5 6 [straight phi] = P P is pressure ratio of the turbine 2, 1 4 1 τ = T T is temperature ratio, 2 t η is efficiency of the turbine 2, and ( ) ( ) . 2 1 2 2 2 ln 1 ln 1 D t p t t t e = C T ?? -η ψ -m [straight phi] ?? is exergy loss of the turbine 2.

For the combustion chamber, the following expression can be obtained:

... (4)

where: ...

For the regenerator, the following expression can be obtained:

... (5)

where

... pressure recovery coefficients.

For the heat exchanger, the following expression can be obtained:

... (6)

where: ... is pressure-recovery coefficient.

For the compressor 2, the following expression can be obtained:

... (7)

where ... is specific work consumed of the compressor 2, 2 c η is efficiency of the compressor 2, ... is exergy loss of the compressor 2, ... and ... is pressure ratio of the compressor 2.

For the exhaust gas of the inverse Brayton cycle, the following expression can be obtained:

... (8)

where ... is exergy loss of the exhaust gas, and ....

For the turbine 1 is solely used to power the compressor 1 ( ... ), one can derive the following expression:

... (9)

For the total pressure ratios of expansion and compression are equal ( 2 1 2 1 / t c c t [straight phi] = D[straight phi] [straight phi] [straight phi] ), one can derive the following expression:

... (10)

where D = D0D1D2D3D4 is total pressure-recovery coefficient.

The specific work and the exergy efficiency of the combined cycle are defined as:

... (11)

... (12)

where ....

To optimize the exergy efficiency, one can derive the following expression from the extremal condition of ....

The optimal pressure ratio of the compressor 2 corresponding to the optimal exergy efficiency is:

... (13)

And the optimal exergy efficiency is:

... (14)

The minimum dimensionless total exergy loss is:

... (15)

4. Numerical examples

In the calculations, it is set that ηc1 =ηc2 = 0.9 , 1 2 0.85 t t η =η = , 1 T = 288.15K , 1 P = 0.1013MPa , 9 P = 0.104MPa , 0.98 i D = ( i = 1, 2,3, 4 ), ε = 0.9 and 0.9 R E = . To see the effects of various parameters on exergy efficiency and other performances of the combined cycle, the results are presented graphically.

Figure 3 shows the influences of the effectiveness ( R E ) of the regenerator on the 1 ( ) E opt c η -[straight phi] and 1 min 1 ( /( )) loss P c e C T -[straight phi] characteristics, respectively. In the range of less than the critical pressure ratio of compressor 1, the optimal exergy efficiency ( ) E opt η increases with the increase in R E and the minimum exergy loss 1 min ( /( )) loss P e CT decreases with increase in R E . It reveals that the regenerator can improve exergy performance of the combined cycle.

Figures 4-7 show the influences of the temperature ratio ( 1 τ ) of the Brayton cycle, the effectiveness (ε ) of the heat exchanger, the pressure-recovery coefficient ( i D ) of each process, the compressor efficiencies ( 1 c η and 2 c η ), as well as the turbine efficiencies ( 1t η and 2 t η ) on the 1 ( ) E opt c η -[straight phi] and 1 min 1 ( /( )) loss P c e C T -[straight phi] characteristics, respectively. They show that the optimal exergy efficiency ( ) E opt η increases with the increases in 1 τ , ε , i D , 1 c η , 2 c η , 1t η and 2 t η . The minimum exergy loss 1 min ( /( )) loss P e CT decreases with increases in 1 τ , ε , i D , 1 c η , 2 c η , 1t η and 2 t η .

Figures 8-12 show the influences of the effectiveness ( R E ) of the regenerator, the temperature ratio ( 1 τ ) of the Brayton cycle, the effectiveness (ε ) of the heat exchanger, the pressure-recovery coefficient ( i D ) of each process, the compressor efficiencies ( 1 c η and 2 c η ), as well as the turbine efficiencies ( 1t η and 2 t η ) on the c2opt c1 [straight phi] -[straight phi] characteristics, respectively. They show that the optimal pressure ratio ( c2opt [straight phi] ) of the compressor 2 increases with the increases in 1 τ , ε , 2 c η , 2 t η , and decreases in R E , i D , 1 c η , and 1t η . They also show that the optimal pressure ratio of compressor 2 will equal to 1 when R E , i D , 1 c η and 1t η are big enough or 2 c η , 2 t η and ε are small enough. In other words, the compressor 2 should be canceled in these extreme conditions.

Figures 13-21 show the influences of the pressure ratio ( 1 c [straight phi] ) of the compressor 1, the effectiveness ( R E ) of the regenerator, the temperature ratio ( 1 τ ) of the Brayton cycle, the effectiveness (ε ) of the heat exchanger, the pressure-recovery coefficient ( i D ), the compressor efficiencies ( 1 c η and 2 c η ), as well as the turbine efficiencies ( 1t η and 2 t η ) on the component irreversibilities for the combined cycle, respectively. They show that the exergy loss of the combustion is the largest, and followed by the exergy loss of the heat exchanger.

5. Conclusion

Exergy analysis and optimization of the combined regenerative Brayton and inverse Brayton cycles with regenerator after the inverse cycle proposed in Ref. [24] has been performed in this paper. The effects of the effectiveness of the regenerator and other parameters on the exergy performances of the combined cycle are analyzed, and the exergy performances are optimized by adjusting the compressor pressure ratio of the bottom cycle. One can see that the base cycle (combined Brayton and inverse Brayton cycle proposed in Ref. [20]) with regenerator can obtain better exergy performance than that of the base cycle. It presents facilitates the design and optimization of complex cycles by pinpointing the exergy losses. The exergy loss of combustion chamber is the largest in the combined cycle and followed by heat exchanger.

Acknowledgments

This paper is supported by The National Natural Science Foundation of P. R. China (Project No. 10905093).

References

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