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Efficient-ecological-function analyses and multi-objective optimizations for generalized irreversible Carnot heat pumps
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DOI：10.1016/j.physa.2025.130979.png)
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Abstract
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Previous studies proposed exergy-based efficient-ecological-function ( Eφ) as a new cycle performance index. In this study, Eφ is introduced into a generalized irreversible Carnot heat-pump (CHP) cycle with heat-leak rate ( q), heat-transfer loss and internal-irreversibility-factor ( Φ). Cycle performances working under the maximum coefficient-of-performance ( φ), maximum Eφ and maximum ecological-function ( E) conditions are compared firstly. Then, single-, dual-, triple-, and quadruple-objective optimizations for the irreversible CHPs are performed with Eφ, φ, heating load ( π) and E as well as their different combinations as optimization objectives, and working-fluid temperature-ratio ( x) as optimization variable, by utilizing NSGA-II algorithm. Pareto-frontiers (PFs) under different objective combinations are obtained. Finally, the PF value is selected by using three decision-making-methods (DMMs): TOPSIS, LINMAP, and Shannon entropy. With the same objective function combination, the deviation indexes ( Ds) of three DMMs are compared and the optimal scheme is selected according to the smallest D. The results for endoreverisble CHP case are also provided. The findings show that Eφ places greater emphasis on the trade-off among φ, π, exergy-output-rate, and entropy-generation-rate. Heat-leak-rate transforms curve of Eφ−φ from parabolic to loop-shaped. The curve of Eφ−π is parabolic shape, Eφ decreases with increases of q and Φ. In practical heat-pump design, it is necessary to choose a designing point with higher φ and π in order to improve performance. On the PF, each point represents an optimal equilibrium-state achieved by objective function. For four-objective optimization, the optimal x ( xopt) for the generalized irreversible CHP cycle ranges between 0.768 and 0.866, while the xopt of endoreversible CHP cycle is between 0.765 and 0.866, which mean the optimal selecting ranges of working-fluid temperature-ratio for the two CHP cycle models. The important contributions herein are introducing Eφ into generalized irreversible CHP and performing multi-objective optimizations with 15 objective combinations considering four performance indicators.
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