A potent numerical model coupled with multi-objective NSGA-II algorithm for the optimal design of Stirling engine

et al. 2022

Two-stage thermoelectric generators have been widely used in the aerospace, military, industrial and daily life fields. Based on the established two-stage thermoelectric generator model, this paper further studies its performance. Applying the theory of finite-time thermodynamics, the efficient power expression of the two-stage thermoelectric generator is deduced firstly. The maximum efficient power is obtained secondly by optimizing the distribution of the heat exchanger area, distribution of thermoelectric elements and working current. Using the NSGA-II algorithm, multi-objective optimizations of the two-stage thermoelectric generator are performed thirdly by taking the dimensionless output power, thermal efficiency and dimensionless efficient power as objective functions, and taking the distribution of the heat exchanger area, distribution of thermoelectric elements and output current as optimization variables. The Pareto frontiers with the optimal solution set are obtained. The results show that when the total number of thermoelectric elements is increased from 40 to 100, the maximum efficient power is decreased from 0.308W to 0.2381W. When the total heat exchanger area is increased from 0.03m2 to 0.09m2, the maximum efficient power is increased from 0.0603W to 0.3777W. The deviation indexes are 0.1866, 0.1866 and 0.1815 with LINMAP, TOPSIS and Shannon entropy decision-making approaches, respectively, when multi-objective optimization is performed on three-objective optimization. The deviation indexes are 0.2140, 0.9429 and 0.1815 for three single-objective optimizations of maximum dimensionless output power, thermal efficiency and dimensionless efficient power, respectively.

Section: Introductionmentioning

confidence: 99%

Maximum Efficient Power Performance Analysis and Multi-Objective Optimization of Two-Stage Thermoelectric Generators

Tian

et al. 2022

“…In order to take different performance indicators into account and obtain the optimal design scheme, Deb et al [ 90 ] proposed the non-dominated sorting genetic algorithm II (NSGA-II), which overcame the three shortcomings of NSGA, including the high computational complexity of non-dominated sorting, the lack of elite strategies, and the need to specify shared parameters. NSGA-II was widely used for the multi-objective optimization (MOO) of various thermodynamic cycles [ 91 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 ]. The Brayton cycle [ 91 ] and Stirling-Otto combined cycle [ 92 ] were optimized by MOO, and the utilized optimization objectives were power output and thermal efficiency; the optimization results were obtained and compared by applying different decision-making approaches.…”

Section: Introductionmentioning

confidence: 99%

“…The ESE heat engine [ 96 ] was optimized by MOO and the utilized optimization objectives were ecological function, power output, efficient power, and thermal efficiency. Stirling engines [ 97 , 98 ], the membrane reactor [ 99 ], and the bidirectional-ribbed microchannel [ 100 ] were also optimized by applying MOO; and the schemes with less contradictions and conflicts were obtained.…”

Section: Introductionmentioning

confidence: 99%

Four-Objective Optimizations of a Single Resonance Energy Selective Electron Refrigerator

et al. 2022

According to the established model of a single resonance energy selective electron refrigerator with heat leakage in the previous literature, this paper performs multi-objective optimization with finite-time thermodynamic theory and NSGA-II algorithm. Cooling load (R¯), coefficient of performance (ε), ecological function (ECO¯), and figure of merit (χ¯) of the ESER are taken as objective functions. Energy boundary (E′/kB) and resonance width (ΔE/kB) are regarded as optimization variables and their optimal intervals are obtained. The optimal solutions of quadru-, tri-, bi-, and single-objective optimizations are obtained by selecting the minimum deviation indices with three approaches of TOPSIS, LINMAP, and Shannon Entropy; the smaller the value of deviation index, the better the result. The results show that values of E′/kB and ΔE/kB are closely related to the values of the four optimization objectives; selecting the appropriate values of the system can design the system for optimal performance. The deviation indices are 0.0812 with LINMAP and TOPSIS approaches for four-objective optimization (ECO¯−R¯−ε−χ¯), while the deviation indices are 0.1085, 0.8455, 0.1865, and 0.1780 for four single-objective optimizations of maximum ECO¯, R¯, ε, and χ¯, respectively. Compared with single-objective optimization, four-objective optimization can better take different optimization objectives into account by choosing appropriate decision-making approaches. The optimal values of E′/kB and ΔE/kB range mainly from 12 to 13, and 1.5 to 2.5, respectively, for the four-objective optimization.

“…Shakouri et al [ 65 ] performed MOO research on solid oxide fuel cell-SHE cycles with three OOs of

, exergy efficiency, and exergy destruction density. Ahmed et al [ 66 ] considered such parameters as heat-source temperature, engine frequency, average effective pressure, piston diameter, and regenerator grid line diameter, and took

, and losses as OOs to perform MOO on SHE cycles.…”

Section: Introductionmentioning

confidence: 99%

“…Compared with the previous MOO research of different SHE cycles [ 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 69 ], the major contribution of this paper is that, firstly, the effects of the linear phenomenological HTL, which is different from Newton’s HTL, on the performance of the SHE are studied, and the expressions of four OOs are derived. It is also found that

, and

are obviously different from those in reference [ 69 ] referring to Newton’s HTL; secondly, a more realistic cycle model with various heat and mechanical losses is adopted; and, finally, different OOs are introduced.…”

Section: Introductionmentioning

confidence: 99%

Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law

et al. 2022

This paper combines the mechanical efficiency theory and finite time thermodynamic theory to perform optimization on an irreversible Stirling heat-engine cycle, in which heat transfer between working fluid and heat reservoir obeys linear phenomenological heat-transfer law. There are mechanical losses, as well as heat leakage, thermal resistance, and regeneration loss. We treated temperature ratio x of working fluid and volume compression ratio λ as optimization variables, and used the NSGA-II algorithm to carry out multi-objective optimization on four optimization objectives, namely, dimensionless shaft power output P¯s, braking thermal efficiency ηs, dimensionless efficient power E¯p and dimensionless power density P¯d. The optimal solutions of four-, three-, two-, and single-objective optimizations are reached by selecting the minimum deviation indexes D with the three decision-making strategies, namely, TOPSIS, LINMAP, and Shannon Entropy. The optimization results show that the D reached by TOPSIS and LINMAP strategies are both 0.1683 and better than the Shannon Entropy strategy for four-objective optimization, while the Ds reached for single-objective optimizations at maximum P¯s, ηs, E¯p, and P¯d conditions are 0.1978, 0.8624, 0.3319, and 0.3032, which are all bigger than 0.1683. This indicates that multi-objective optimization results are better when choosing appropriate decision-making strategies.