Thermodynamic analysis and multi objective optimization of performance of solar dish Stirling engine by the centrality of entransy and entropy generation

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Highlights

  • Thermodynamic analysis of solar dish Stirling engine is performed.

  • The latter is achieved using NSGA II algorithm.

  • The final optimal solution has been selected using three decision-making methods.

  • Error analysis was performed based on the average error and the maximum error.

Abstract

This paper makes attempts to perform multi-objective optimization on the solar-powered Stirling engine with high temperature differential. A new model was proposed based on the finite-time thermodynamic. Furthermore, the thermal efficiency of the solar Stirling system with a rate of finite heat transfer, regenerative heat loss, the output power, finite regeneration process time and conductive thermal bridging loss is specified. The thermal efficiency, entransy loss rate and power output have been maximized simultaneously for a dish-Stirling system and entropy generation’s rate in the engine minimized via using thermodynamic analysis and NSGA-II algorithm. To specify the optimum values of the above mentioned parameters three well known decision making methods have been employed. Finally, an error analysis was applied on the outputs gained from each decision makers.

Introduction

One of the vital and straightforward standard air cycles for heat engines is addressed to Stirling cycle [1], [2]. With the aim of profits of the aforementioned cycle, an adequate efficiency can be specified and extend variety of fuels can be implemented for heating purposes. [2], [3], [4]. From theoretical point of view, at the Carnot efficiency, the Stirling engine can be a high performance engine to change heat into the mechanical work when the isothermal expansion and compression processes and ideal regeneration are involved. Working temperatures of the cooler and heater sides ply a crucial role on the thermal restriction for the operational condition of a Stirling engine. Through most cases, the operational temperatures of the aforementioned engine are 923 K and 338 K for heater and cooler temperature, correspondingly [5]. Efficiency of Engine changes from 30% to 40% that belongs to a general temperature boundary of 923–1073 K, and span of the normal operating varies from 2000 to 4000 rpm [6], [7], [8], [9], [10], [11]. Incorporation of solar concentrators and Stirling engines is a novel thought that facilitates changing the solar energy into the electric power. Through this instance, parabolic layers of the mirrors are utilized with a dish collector to concentrate the solar radiations throughout a central spot of the collector in which the absorber of heat is fixed. Aksoy and Cinar [12] made attempt to determine the impact of the grooved displacer cylinder on engine performance from thermodynamic and kinematic viewpoints. Chen et al. [13] experimentally investigated a helium charge c-type twin power piston Stirling engine to specify the impacts of different regenerator variables on the overall performance of the engine.

Four different types of CSP plants which are currently employed: Linear Fresnel Reflectors, Parabolic Troughs, Power Tower and Stirling Dish systems. It is worth to mention that regardless of their different setups, their primary mechanism is similar; reflection of sunlight onto a central receiver. Between the abovementioned types, the Stirling dish has the highest efficiency about 27% [14]. All dish Stirling system distributions are demonstrated in [15], [16], [17]. Through last two decades, eight different dish-Stirling systems in the range of 2–50 kW were created by companies in the Germany, United States, Russia and Japan [18]. A scheme with installed capacity 1.5 MW is in process in Peoria, AZ, and plats with graded capacity of several hundred megawatts are in the designing phases [19]. There are few more large plans presently under designing and building which are worth prominence because of their noteworthy power size. These plans are located in the United States with an installed capacity of 750 and 850 MW and in India using Infinia Corp, employ Stirling Energy Systems technology. Technology with a capacity of 9–10 MW [20]. Chen and colleagues have proposed FTT analysis to optimize the performance of a solar powered Stirling engine [21].

Through the recent years, enormous efforts have been put forth to specify the optimal performance of solar-driven energy systems, with the aim of the analysis of the finite time thermodynamic (FTT) [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47]. Solutions gained from the aforementioned thermodynamic analysis are more reliable than other thermodynamic approaches. Thanks to this fact, the upshots are highly discerned to improvise the real optimal solar energy systems draw in parallel with the previous approaches.

Yaqi et al. [23] performed finite-time thermodynamics to determine optimum values of parameters through a solar-powered Stirling heat engine. The primary regular operating conditions for a solar thermal power plant in expression of rate of finite heat transfer and a process with internally reversibility throughout illuminated a number of parametric formulas is specified by Lund [29]. The optimum operational statuses of a Carnot-type irreversible solar-powered heat engine with the radiation overcome heat transition between the source of heat and fluid of working as well as the convection overcome heat transition between the sink of heat and fluid of working are carried out by Tamer Yilmaz et al. [30].

A finite-time factor as the proportion of the contact time of working fluid to the time constant of the engine which develops the heat transfer characteristics of the aforementioned Stirling engine project is specified by Ibrahim and Ladas [34]. They conducted a numerical investigation and schemed the variation of the power output against efficiency, the alteration of the power output against the finite-time factors and outcomes of the regeneration. Sieniutycz and von Spakovsky securitized the thermal exergy with the aim of the finite-time approach [38]. A smart thermo-economic research on the basis of the objective function stand for the power output per unit total cost is proposed by Kodal and Sahin [39].

A thought of the possible performance for an actual engine is illustrated by Blank and collaborators [42] throughout checking the optimization of power in the endoreversible Stirling cycle. The equivalence of energy of a self-determining solar power plant with a Stirling engine is thorough by Trukhowet and collaborators [43]. It is represented that the electric power output is depends on the direction of solar radiation. The size of engine restricts and Chen and colleagues are investigated the efficiency of a solar driven Stirling heat engine at the maximum output power [44].

The entransy theory is recently progressed and is applied to heat transfer optimizations. Guo and colleagues [48] suggested the entransy concept from the comparison between the heat and electric conduction. According to this concept, Guo and colleagues established the extremum ED phenomenon and theory of the minimum entransy-dissipation on the basis of the thermal resistance. These origins are implemented to optimize heat transfer such as conduction and convection [49], [50], [51], [52], [53], thermal radiation [54], [55] and the design of the heat exchangers [56], [57].

For the concept of entransy dissipation (ED), researches show that it is not appropriate for optimizing the processes of heat-work conversion [58], [59]. However, efforts are made to extend the application of the entransy theory to the optimization of the heat-work conversion.

Cheng and colleagues [60], [61], [62] suggested the entransy loss (EL) concept, which is the sum of ED owing to the entransy variation thanks to the work output and the irreversible heat transfer. EL is the entransy that is employed in the heat-work conversion processes.

To indicate solution of the multi-objective optimization issues, huge amounts of efforts required to assure parallel and different objectives; however, may be conflict each other. Through previous decades evolutionary algorithms (EA) have been primarily utilized to stochastically unravel issues of this general category [63]. An appropriate outcome of a multi-objective issue is to specify an assortment of results, each of that assures the objectives at an adequate degree without being prevailed by any other result [64]. Optimizing Multi-objective issues in general depict a feasible countless assortment of outcomes known as frontier of Pareto, where examined vectors denote the best feasible trade-offs throughout the objective function region. Owing to this point, optimizing with multi-objective optimization of various energy systems and thermodynamic were carried out by different researchers [65], [66], [67], [68], [69], [70], [71], [72]. Arora and colleagues [71] made attempt to optimize thermal efficiency, triple power and thermo-economic function in solar powered Stirling heat engine based on NSGAII algorithm and FTT analysis. Ahmadi et al. [73], [74], [75], [76], [77], [78], [79] developed an intelligent approach to figure power of solar Stirling heat engine by implementation of evolutionary algorithms.

This work includes two scenarios, in the first scenario by executing multi-objective optimization approach, the Stirling engine’s thermal efficiency and the output power and entransy loss rate of system are maximized; in the second scenario, output power and entransy loss rate of the system are maximized, entropy generation’s rate of the solar-dish Stirling engine is also minimized by using the same approach. Moreover, the ultimate results of aforementioned processes have been drawing and compared with experimental data reported in [23]. Finally, analysis of error has been carried out to specify precision and robustness of ultimate outputs of each decision making techniques.

Section snippets

Thermodynamic analysis of the system

As shown in Fig. 1, four different processes constitute the Stirling cycle. An isothermal process is addressed to Process 1–2, where the working fluid of compression at consistent temperature, Tc, releases the heat into the heat sink at fixed temperature, TL. After that in an isochoric process 2–3, the fluid of working passes the regenerator and becomes warm to Th. In next stage, the working fluid spreads out at a consistent temperature, Th, and gains the heat from the source of heat at a

Optimization via EA

Throughout the present work, the frontier of Pareto is specified by executing Genetic Algorithm (GA) which is a chapter of evolutionary approach. John Holland in the 1960s is a first scientist that proposed and evolved the GA as a tool of numerical optimization with the inspiration of natural evolution of Darwin’s theorem and converting it into computer program [65]. They are executed as a PC simulator approach where a population of digest illustrations of volunteer outcomes to an optimization

Results and discussion

The dimensionless output power (P) and thermal efficiency of the solar-dish Stirling system (ηm) and entransy loss rate are maximized in parallel and entropy generation’s rate of the engine are also minimized in parallel by executing the multi-objective optimization technique that developed on the basis of the NSGA-II process. Thanks to this fact, aforementioned approach is applied on the suggested functions that considered as objective functions which are formulated by Eqs. (18), (19), (20),

Conclusion

To optimize the thermal efficiency, output power, entropy generation’s rate and entrance loss rate of the solar dish-Stirling engine, finite-time thermodynamics and multi-objective optimization has been employed. Various variables, including conductive heat transfer mechanism at source of heat, sink of heat in the engine and dish collector performance have been considered in this paper. In the first scenario, the thermal efficiency, output power and entransy loss rate of the engine has been

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