Multi-objective thermo-economic optimization of solar parabolic dish Stirling heat engine with regenerative losses using NSGA-II and decision making
Introduction
Solar energy is one of clean renewable source of energy which reduces dependability of human needs on fossil fuels and hazards caused to environment with usage of these fuels [1]. The idea of using solar energy as input energy source for heat engines has been applied by coupling solar concentrators with Stirling heat engine for useful power output [2]. The use of solar driven Stirling engine for power output source is continuously increasing because of its environment friendly nature compared to internal combustion engines. Blank et al. [3] performed power optimization of endoreversible Stirling heat engine. They estimated maximum possible power output of real engine under predetermined circumstances. Chen et al. [4] studied solar driven Stirling heat engine to find out its maximum possible efficiency. Kaushik et al. [5], [6], [7], [8] implemented finite time thermodynamic approach on endoreversible [5] and irreversible [6], [7], [8] Stirling/Ericsson cycles and found that at regenerator effectiveness of one, Stirling heat engine could perform as Carnot heat engine provided both are operating in endoreversible mode. They also found that maximum power output of Ericsson and Stirling engines are independent of heat losses due to regenerator, effectiveness of regenerator and direct heat leak between heat source and heat sink. Tyagi et al. [9] incorporated internal irreversibility parameter while defining ecological function of Stirling and Ericsson cycles implementing finite time thermodynamic approach. They carried out analysis of the impact caused by internal irreversibility parameter on ecological function, power output and thermal efficiency of both cycles. Kongtragool and Wongwises [10] investigated Stirling heat engine and found that maximum power output and corresponding thermal efficiency decreases with increase in irreversibilities in the system. Tlili et al. [11] developed theoretical model for calculating net-work output, thermal efficiency and heat addition in view of first law of thermodynamics with internal irreversibility. Furthermore, Tlili [12] evaluated Stirling heat engine through endoreversible mode for maximum power conditions implementing finite time thermodynamic approach. Costea et al. [16] analyzed the effect of irreversibilities on solar Stirling cycle performance by using a mathematical model based on first law of thermodynamics for processes with finite speed. Petrescu et al. [17] calculated the efficiency and power output of Stirling engine implementing direct method. Analytical models based on polytropic expansion/compression processes for predicting thermal performance of Stirling engines are developed and classified as first order [18] closed form, second order [19], [20], [21] zero dimensional numerical model. Hosseinzade and Sayyaadi [22] carried out combined adiabatic and finite speed thermodynamic analysis while considering effect of finite speed, pressure drop and mechanical friction of piston. The existing literature shows the evaluation of power output [3], thermal efficiency [4], thermo-economic function [13], [14], [15] and ecological function [9] under single objective optimization approach. However, practical designing mandates optimization of two or more objective functions at the same time. Few research investigations are available for multi-objective optimization of various thermal energy conversion systems [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]. Further, optimization of various design and input parameters using evolutionary algorithm in thermal modeling of solar powered Stirling engines has been carried out by Refs. [34], [35], [36], [37], [38].
In view of this, thermo-economic optimization of proposed system with regenerative losses and cycle irreversibility parameter has been carried out by the authors. Thermo-economic function chosen as one of the objective in this study includes annual investment cost, energy consumption cost and maintenance cost. Here, a dish collector with parabolic arrangement of mirrors have collected solar energy on a focal point of the collector and acts as a high grade input heat energy for Stirling engine. Performance analysis and multi-objective optimization of solar parabolic dish Stirling heat engine has been done for simultaneous optimization of power output, thermal efficiency and thermo-economic function. Multi-objective optimization is helpful in designing real heat engine as it provides a trade-off between the obtained solutions of various chosen objectives with minimum computation time. The major outcome of this research is the evaluation of specific optimal points for various input parameters viz. effectiveness of source-side heat exchanger (εH), effectiveness of sink-side heat exchanger (εL), effectiveness of regenerator-side heat exchanger (εR), heat source temperature (TH1), source side temperature of working fluid (Th), sink side temperature of the working fluid (Tc). The authors have also found the optimal value of average absorber temperature and concentration ratio as 1168.1 K and 1300.7 respectively. The present work shows triple objective (P–η–F) and dual objective (P–η, P–F) optimization for solar parabolic dish Stirling heat engine based on NSGA-II. The Pareto frontier in objective space is achieved based on evolutionary algorithm. The optimal values of various input parameters are chosen from Pareto frontier implementing four decision making including Fuzzy, TOPSIS, Shannon’s entropy and LINMAP methods. The effects of various parameters on triple objective have been studied in detail and the results are presented on graphs.
Section snippets
System description
A solar powered Stirling heat engine is shown in Fig. 1. It comprises of mirrors arranged in parabolic fashion to form a dish collector and thermal absorber on the focal point where collector collects all the solar radiations. A cavity absorber is created at the focal point which transfers collected solar energy to the working fluid in engine’s displacer hot end. The solar dish is equipped with a sun tracker which tracks the sun in order to have maximum solar energy transfer to the engine when
Thermodynamic analysis
Stirling heat engine model 1–2–3–4–1 with real compression and expansion processes is developed based on the following assumption:
- (a)
The radiation and convection heat transfer between absorber and working fluid and convective heat transfer between heat sink and working fluid are included in the analysis.
- (b)
Finite heat capacity heat source and heat sink are considered.
- (c)
The irreversibilities due to regenerative heat losses, conductive thermal bridging losses and finite regeneration process time are
Multi-objective optimization
Decision making techniques are used to obtain final optimal solution from Pareto frontier in multi-objective optimization algorithms. Before the application of any decision making process, it is mandatory to unify the dimension and scale of all the objectives correspondingly. For this, objective vectors need to be non-dimensionalized using linear, Euclidean and fuzzy non-dimensioned methods as discussed below.
Linear non-dimensionalization approach:
Objective function(s) can be made
Results and discussion
The optimal value of power output, thermal efficiency and thermo-economic function is obtained implementing evolutionary algorithm based on NSGA-II. The final optimal solution selected by Fuzzy, TOPSIS, Shannon’s entropy and LINMAP decision making methods are shown on original Pareto frontier in Fig. 5. The ideal and nadir solution for triple objectives (P–η–F) optimization of solar parabolic dish Stirling heat engine are 39.43 kW, 0.2718, 0.3336 and 35.80 kW, 0.2296, 0.3056 respectively.
Conclusion
Multi-objective thermo-economic optimization of solar parabolic dish Stirling heat engine has been carried out. Power output, thermal efficiency and thermo-economic function are considered as three objectives to obtain the Pareto frontiers for triple and dual objective optimization. The best optimal values are obtained using four decision making methods viz. Fuzzy Bellman-Zadeh, TOPSIS, Shannon’s and LINMAP. Similarly, deviation index of each solution from the ideal one is obtained. It is found
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