# Exergy Analysis and Second Law Efficiency of a Regenerative Brayton Cycle with Isothermal Heat Addition

## Abstract

**:**

## Introduction

_{p}of 12:1. Therefore, the use of regeneration to improve the thermal efficiency of Brayton cycles with isothermal heat addition should be carefully checked [1]. Erbay et al [2], used the maximum power density method to determine the optimal operating conditions of the regenerative Brayton gas turbine engine with isothermal heat addition. They found that the low efficiency problem noted for the regenerative Brayton cycles has been eliminated by the isothermal heat addition. Tyagi et al [3], carried out an ecological function optimization of an irreversible regenerative Brayton cycle with isothermal heat addition along with real processes using the concept of finite time thermodynamics. They indicated that the ecological is an increasing function of the components efficiencies, the effectiveness and the temperature on the isothermal-, sink- and regenerative –side heat exchangers while it is found to be a decreasing function of the working fluid heat capacitance rate and the temperature and effectiveness on the isobaric –side heat exchanger. Kaushik et al [4], studied the effect of various parameters on the performance of the Brayton heat engine and showed that there is a significant improvement in the performance of Brayton cycle (above 15 %) with isothermal heat addition over the conventional cycle. Wang et al [5], explained that there exists an optimal total pressure ratio that leads to a double-maximum power output. An optimal cycle working range, i.e. high power output and high efficiency, can be obtained according to the characteristic of the maximum power versus its corresponding efficiency. Many authors in the recent years carried out the exergy analysis of various thermal systems. Zheng et al [6], demonstrated the effect of various parameters on the exergy performance for a Braysson cycle and conclude that the specific work and exergy efficiency of the Braysson cycle are larger than those of Brayton cycle under the same conditions. Rosen and D’ncer [7], brought into view that the potential usefulness of exergy analysis in addressing and solving energy-related sustainable development and environmental problems is substantial, and that exergy is a confluence of energy, environment and sustainable development. An exergy-costing method was developed by assigning a single unit cost to a specific exergy, regardless of the type of exergy stream and state of the stream. This methodology provides some information that is related to the actual production process within the system, Kim et al [8]. The effect of various parameters, such as gas turbine pressure ratio, turbine inlet temperature and others, on the exergy performance of a gas-turbine combined-cycle power plant was presented by Ertesvag et al [9]. Very important conclusion about exergetics is found in the study of Mei Gong and Goran Wall [10], exergy is a useful concept since it is a link between the physical and engineering world and the surrounding environment. Exergy also expresses the true efficiency of engineering systems; therefore, it is strongly recommended that exergy is used in the design of engineering systems. The second law of thermodynamics may well turn out to be the central scientific truth of the twenty-first century. Nothing disappears and every thing disperses, so exergy is a suitable and necessary concept in the development of a sustainable society Wall [11].

## Theoretical model

_{6}. In an ideal regenerator, the gas will leave the regenerator at the same temperature of the turbine exhaust T

_{5}. The isobaric heat addition process takes place in the regular combustion chamber (RCC) between states 6 and 3. Extra heat addition is accomplished isothermally in the CCC between states 3 and 4. The gas leaving the CCC at state 4 with a lower pressure than that at state 3, but the velocity, and consequently the kinetic energy, of the gas has been increased due to the nature of the CCC. The gas then expands in the turbine to state 5. The hot gases enter the regenerator, where it is cooled isobarically to state 7. The cycle is completed by cooling the gas to the initial state. The processes 1-2s and 4-5s are isentropic compression and expansion.

- -
- Compressor:
- -
- Regenerator:
- -
- Regular combustion chamber:
- -
- Converging combustion chamber:
- -
- Turbine:
- -
- Exhaust:
- -
- The whole cycle:$${\eta}_{II}=\frac{{\eta}_{th}}{{\eta}_{th,rev}}$$

## Results and discussion

_{t}. Analysis of such modified cycle has shown that the parameter r

_{t}has a strong effect on the validity of the second law of thermodynamics. From Eq. (12), the first term is zero, because T

_{4}= T

_{3}, then for positive entropy generation

_{t}than 0.7308194 will violate the second law of thermodynamics. Taking this into account, r

_{t}is assumed to be o.65 in this study.

_{p}is calculated at the average temperature of each process separately, by iteration.

- A-
- Ideal air-standard simple cycle,
- B-
- Simple cycle with loses,
- C-
- Regenerative air cycle,
- D-
- Air cycle with isothermal heat addition,
- E-
- Regenerative air cycle with isothermal heat addition,

_{p}/ C

_{v}, which is calculated accordingly with the appropriate value of C

_{p}. A reference “design” point of the cycles is assumed to be as follows: r

_{p}= 10, TIT = 1104 K, ambient and dead state conditions are P = 1.01325 bar, T

_{0}= 300 K. For Mach numbers, the values assumed in Vecchiarelli et al. [12] are used, that is M

_{3}= 0.2 and M

_{4}= 0.8 .

D. P. | |||||||||

r_{p} | 1 | 2 | 3 | 4 | 5 | 10 | 15 | 20 | 25 |

TIT[K] | 850 | 900 | 950 | 1000 | 1050 | 1104 | 1150 | 1200 | 1250 |

T_{0}[K] | 275 | 280 | 285 | 290 | 295 | 300 | 305 | 310 | 315 |

P[bar] | 0.9546 | 0.9546 | 0.8456 | 0.795 | 0.7469 | 1.01325 | 0.7012 | 0.6578 | 0.6166 |

Alt.[m] | 0 | 500 | 1000 | 1500 | 2000 | 2500 | 3000 | 3500 | 4000 |

P[bar] | 1.01325 | 0.9546 | 0.8988 | 0.8456 | 0.795 | 0.7469 | 0.7012 | 0.6578 | 0.6166 |

T_{0}[K] | 288.15 | 284.9 | 281.7 | 278.4 | 275.2 | 271.9 | 268.7 | 265.4 | 262.2 |

## Conclusions

Nomenclature | |

c | Speed of sound, m/s |

C_{p} | Constant pressure specific heat, kJ/kg.K |

C_{v} | Constant volume specific heat, kJ/kg.K |

g | Gravitational acceleration, m/s^{2} |

h | Specific enthalpy, kJ/kg |

k | Specific heat ratio |

$\stackrel{\xb7}{m}$ | Mass flow rate,kg/s |

M | Mach number |

P | Pressure, kPa |

q | Heat transfer per unit mass flow, kJ/kg |

$\stackrel{\xb7}{{Q}_{k}}$ | Heat transfer rate through the boundary at temperature T_{k} at location k, kW |

r_{p} | Pressure ratio |

R | Gas constant, kJ/kg.K |

s | Specific entropy, kJ/kg.K |

s_{gen} | Specific entropy generation, kJ/kg.K |

${\stackrel{\xb7}{S}}_{gen}$ | Entropy generation rate, kW/K |

T_{0} | Surroundings temperature, K |

T_{in} | Temperature of the source from which the heat is transferred to the working fluid |

T_{k} | Temperature of location k from which the heat $\stackrel{\xb7}{{Q}_{k}}$ is transferred to the working fluid |

T_{max } | Maximum temperature of a cycle |

T_{min} | Minimum temperature of a cycle |

TIT | Turbine inlet temperature |

v | velocity, m/s |

$\stackrel{\xb7}{W}$ | Power, kW |

x_{destroyed} | Specific exergy destruction, kJ/kg |

${\stackrel{\xb7}{X}}_{destroyed}$ | Rate of total exergy destruction, kW |

z | Elevation, m |

Greek Letters | |

${\eta}_{th}$ | Thermal efficiency |

${\eta}_{th,rev}$ | Thermal reversible efficiency |

${\eta}_{II}$ | Second-law efficiency |

$\psi $ | Stream exergy, kJ/kg |

Subscripts | |

c | Compressor |

CCC | Converging combustion chamber |

exh | Exhaust |

reg | Regenerator |

RCC | Regular combustion chamber |

t | Turbine |

## References

- Goktun, S.; Yavus, H. Thermal efficiency of a regenerative Brayton cycle with isothermal heat addition. Energy conversion & management
**1999**, 40, 1259–1266. [Google Scholar] - Erbay, L. B.; Goktun, S.; Yavus, H. Optimal design of the regenerative gas turbine engine with isothermal heat addition. Applied energy
**2001**, 68, 249–264. [Google Scholar] [CrossRef] - Tyagi, S. K.; Kaushik, S. C.; Tiwari, V. Ecological Optimization and parametric study of an irreversible regenerative modified Brayton cycle with isothermal heat addition. Entropy
**2003**, 5, 377–390. [Google Scholar] [CrossRef] - Kaushik, S. C.; Tyagi, S. K.; Singhal, M. K. Parametric study of an irreversible regenerative Brayton cycle with isothermal heat addition. Energy conversion & management
**2003**, 44, 2013–2025. [Google Scholar] - Wang, W.; Chen, L.; Sun, F.; Wu, C. Power optimization of an irreversible closed intercooled regenerative Brayton cycle coupled to variable-temperature heat reservoirs. Applied thermal engineering
**2005**, 25, 1097–1113. [Google Scholar] [CrossRef] - Zheng, J.; Sun, F.; Chen, L.; Wu, C. Exergy analysis for a Braysson cycle. Exergy, an International journal
**2001**, 1(1), 41–45. [Google Scholar] [CrossRef] - Rosen, M.; D’ncer, I. Exergy as the confluence of energy, environment and sustainable development. Exergy, an International journal
**2001**, 1(1), 3–13. [Google Scholar] [CrossRef] - Kim, S.; Oh, S.; Kwon, Y.; and Kwak, H. Exergoeconomic analysis of thermal systems. Energy
**1998**, 23(5), 393–406. [Google Scholar] [CrossRef] - Ertesvag, I. S.; Kvamsadal, H. M.; Bolland, O. Exergy analysis of a gas-turbine combined-cycle power plant with precombution CO
_{2}capture. Energy**2005**, 30, 5–39. [Google Scholar] [CrossRef] - Gong, M.; Wall, G. On exergetics, economics and optimization of technical processes to meet environmental conditions. In TAIES’97 International conference on
**T**hermodynamic**A**nalysis and**I**mprovement of**E**nergy**S**ystems, Beijing, China, June 10-13, 1997. published in Cai, Ruixian; et al. (Eds.) Thermodynamic Analysis and Improvement of Energy Systems; pp. 453–460. Beijing World, Chinese Society of Engineering Thermodynamics and American Society of Mechanical Engineering, 1997. - Wall, G. Conditions and tools in the design of energy conversion and management systems of a sustainable society. Energy conversion and management.
**2002**, 43, 1235–1248. [Google Scholar] [CrossRef] - Vecchiarelli, J.; Kawall, JGce JS. Analysis of a concept for increasing the efficiency of a Brayton cycle via isothermal heat addition. International Journal of Energy Research.
**1997**, 21, 113–127. [Google Scholar] [CrossRef] - Cengel, Y. A.; Boles, M. A. THERMODYNAMICS: an engineering approachMcGraw-Hill, Fourth edition; 2002; pp. 391–437. [Google Scholar]

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**MDPI and ACS Style**

Jubeh, N.M.
Exergy Analysis and Second Law Efficiency of a Regenerative Brayton Cycle with Isothermal Heat Addition. *Entropy* **2005**, *7*, 172-187.
https://doi.org/10.3390/e7030172

**AMA Style**

Jubeh NM.
Exergy Analysis and Second Law Efficiency of a Regenerative Brayton Cycle with Isothermal Heat Addition. *Entropy*. 2005; 7(3):172-187.
https://doi.org/10.3390/e7030172

**Chicago/Turabian Style**

Jubeh, Naser M.
2005. "Exergy Analysis and Second Law Efficiency of a Regenerative Brayton Cycle with Isothermal Heat Addition" *Entropy* 7, no. 3: 172-187.
https://doi.org/10.3390/e7030172