Elsevier

Energy Conversion and Management

Volume 134, 15 February 2017, Pages 116-124
Energy Conversion and Management

New exergy analysis of a regenerative closed Brayton cycle

https://doi.org/10.1016/j.enconman.2016.12.020Get rights and content

Highlights

  • The maximum power is studied relating to time and size constraints variations.

  • The influence of time and size constraints on exergy destruction are investigated.

  • The definitions of heat exergy, and second law efficiency are modified.

Abstract

In this study, the optimal performance of a regenerative closed Brayton cycle is sought through power maximization. Optimization is performed on the output power as the objective function using genetic algorithm. In order to take into account the time and the size constraints in current problem, the dimensionless mass-flow parameter is used. The influence of the unavoidable exergy destruction due to finite-time constraint is taken into account by developing the definition of heat exergy. Finally, the improved definitions are proposed for heat exergy, and the second law efficiency. Moreover, the new definitions will be compared with the conventional ones. For example, at a specified dimensionless mass-flow parameter, exergy overestimation in conventional definition, causes about 31% lower estimation of the second law efficiency. These results could be expected to be utilized in future solar thermal Brayton cycle assessment and optimization.

Introduction

The underlying functional point of cyclic heat engines is maximum power state. The operational point in maximum power and reversible performance possess the same importance. The efficiency of heat engines are restricted by Carnot efficiency. This efficiency is obtainable in the reversible case. Practically, all thermodynamic processes take place in finite-size components during finite-time, which leads to irreversibility (exergy destruction). Accordingly, while Carnot cycle gives upper bound for thermal efficiency, it cannot be a comparison standard for real heat engines. Analysis techniques have been developed in various studies to consider the internal and/or external irreversibility in heat engines.

Curzon and Ahlborn [1] studied the effect of external irreversibility, which accounted for irreversibilities in the heat-exchange processes between the power cycle and its heat sources, on Carnot cycle’s output power and thermal efficiency. This system was entitled endoreversible due to internal reversibility of cycle. In their research, thermal efficiency at the maximum power state was expressed in the form of Eq. (1). TL and TH are temperatures at cold and hot heat exchangers, respectively.ηCA=1-TLTH

Bejan [2] showed that the degree of thermodynamic imperfection of power plants could be estimated based on a very simple model that considers only the sources of heat transfer irreversibilities. In a separate study, Bejan [3] investigated the optimal allocation of heat exchange equipment. His study showed that the power output of various power plant configurations could be maximized by properly dividing the fixed inventory of heat exchange equipment among the heat transfer components of each plant. Wu [4] established a comparison between endoreversible Carnot cycle and the same system with both internal and external irreversibility. It was shown that the internal irreversibility reduces power and efficiency.

Gordon [5] analyzed heat engines considering finite rate heat transfer and finite-capacity thermal reservoirs. He showed that the efficiency at maximum power depends on the thermal reservoir temperatures, and other system variables such as reservoir capacity or working fluid specific heats.

Heat engines operate in finite time; therefore, the realistic study of their optimal performance is feasible through the concept of finite-time thermodynamics [6]. This method was applied to the optimization of regenerative endoreversible Brayton cycle with finite thermal capacitance rates in heat reservoirs [8]. In the undertaken research, application of regenerators led to decrease in the maximum power and thermal efficiency. Their study showed the regenerative heat-transfer rate was positive for low temperature ratios and negative for high temperature ratios. Further analyses were performed on regenerative and irreversible models of Brayton heat engines [9], [10].

Optimization of real systems is confined to thermal performance and physical constraints. Bejan [11] established two optimization approaches based on these elements: (i) improving thermal performance subject to physical size constraints (e.g. the minimum entropy generation) and (ii) physical size minimization subject to specified thermodynamic performance. He concluded that both approaches lead to the same physical configuration. Herrera et al. [13] used heat exchanger size as design constraints for irreversible regenerative Brayton cycle optimization. In this model, finite-time thermodynamics and optimization were used to determine the maximum power and minimum entropy generation, along with the global maximum net power.

In various research studies different thermal parameters were used for thermodynamic optimization of heat engines. Power density and exergy density are two of these objective functions, applied to irreversible Brayton cycle with regeneration, and cogeneration system [12], [14]. Parametric design for the maximum exergy density leads to a smaller and more efficient cogeneration system. Yang et al. [15] showed that regeneration and intercooling process can improve the economic profit rate and exergy efficiency of cogeneration plants. Haesli [16] has studied second law efficiency optimization of a regenerative Brayton cycle. He examined the maximum limit of the thermal efficiency of an ideal Brayton cycle, and defined the second law efficiency of the cycle as the ratio of the thermal (first law) efficiency to the maximum attainable efficiency.

Tsatsaronis and Park [17] have divided exergy destruction into avoidable and unavoidable parts and demonstrated how to estimate the avoidable and unavoidable exergy destruction associated with system's components. F. Petrakopoulou et al. [18] analyzed a combined cycle power plant using both conventional and advanced exergetic analyses. They found that most of the exergy destruction in the plant components was unavoidable. Vučković et al. [19] investigated an industrial plant using both conventional and advanced exergy analysis. They claimed that highest exergy destruction was caused by the steam boiler. Moreover 92.34% of the total exergy destruction in boiler was unavoidable. Açıkkalp et al. [20] have analyzed a trigeneration system using an advanced exergy analysis. The results of their research indicated that the improvement potential of their system was low because 82% of the total exergy destruction cost rates were unavoidable. Naserian et al. sought the optimal performance of a regenerative Brayton cycle through multi-objective ecological function maximization [21], and exergoeconomic multi objective optimization [22] using finite-time thermodynamic concept and finite-size components. Goodarzi [23] introduced and then analyzed energetically a new regenerative Brayton cycle.

In current study, an irreversible closed-cycle Brayton engine with regeneration is investigated. Use of a closed-cycle system permits working fluids other than air, such as carbon dioxide [24], Helium [25]. Traditional Brayton cycles can be upgraded to supercritical CO2 to enable much greater efficiencies and power outputs [26]. Many studies have been published on the performance and optimization of the Brayton cycle and solar thermal Brayton cycle [27], [28], [29], [30], [31], [32]. There are other studies that used, Finite time thermodynamic (FTT), power optimization, thermoenvironmental, and ecological methods in evaluation and comparison of thermal cycles [33], [34], [35], [36], [37].

The main originality of the current research is as follows:

  • The maximum attainable dimensionless net output power is obtained considering the impact of mass-flow parameter variation.

  • The influence of dimensionless mass-flow parameter on internal, and external exergy destructions, and 1st and 2nd law efficiencies are investigated.

  • The definitions of heat exergy, and second law efficiency are modified.

Section snippets

Heat engine model

The schematic of the system, an irreversible regenerative closed Brayton cycle, is shown in Fig. 1. The heat engine includes an irreversible compressor, a regenerator, two heat exchangers, and an irreversible turbine. Heat exchangers are used to transfer heat from high temperature flow to the cycle and from the cycle to the low temperature flow. The entire analysis of system can be broken down into: (i) energy analysis (ii) exergy analysis.

Optimization study

For certain values of F, the system is simulated in MATLAB.. Outcome of this modeling is used in genetic algorithm for optimization purpose. Genetic algorithm has been used by several researchers (such as Naserian et al. [21], [22], Ahmadi et al. [25], and Ahmadi et al. [29]) to optimize the operation of thermodynamic cycles. The flowchart of optimization process is shown in Fig. 2. The net output power of system is specified as the objective function for optimization (Eq. (33)).Ẇ=Ė10-Ė9

Results and discussion

Variation of dimensionless net power with parameter F is depicted in Fig. 3 at the maximum power state. Hereafter, all results are investigated at the maximum state even though it is not stated. The slope of power increases gradually with F up to the maximum of maximum power value at F = 0.3. Afterwards, the dimensionless net power slopes down sharply. Therefore, the maximum of maximum net power is located between the two limits.

Exergy of high temperature thermal source, dimensionless input heat

Conclusion

The optimal performance of a closed regenerative Brayton cycle was sought through power maximization. Optimization was performed on the output power as the objective function using genetic algorithm. The optimization was performed based on the dimensionless mass flow rate parameter (F). The behavior of the system variables, such as maximum power, and exergy. were investigated using F. The irreversibilities originating from finite-time and finite-size constraints are unavoidable in the real

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