Efficient-ecological-function analyses and multi-objective optimizations for generalized irreversible Carnot heat pumps

Abstract

Previous studies proposed exergy-based efficient-ecological-function ($E_{\phi }$) as a new cycle performance index. In this study, $E_{\phi }$ is introduced into a generalized irreversible Carnot heat-pump (CHP) cycle with heat-leak rate ($q$), heat-transfer loss and internal-irreversibility-factor ($\Phi$). Cycle performances working under the maximum coefficient-of-performance ($\phi$), maximum $E_{\phi }$ and maximum ecological-function ($E$) conditions are compared firstly. Then, single-, dual-, triple-, and quadruple-objective optimizations for the irreversible CHPs are performed with $E_{\phi }$, $\phi$, heating load ($\pi$) 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 $E_{\phi }$ places greater emphasis on the trade-off among $\phi$, $\pi$, exergy-output-rate, and entropy-generation-rate. Heat-leak-rate transforms curve of $E_{\phi }-\phi$ from parabolic to loop-shaped. The curve of $E_{\phi }-\pi$ is parabolic shape, $E_{\phi }$ decreases with increases of $q$ and $\Phi$. In practical heat-pump design, it is necessary to choose a designing point with higher $\phi$ and $\pi$ 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 $x$ ($x_{\mathrm{opt}}$) for the generalized irreversible CHP cycle ranges between 0.768 and 0.866, while the $x_{\mathrm{opt}}$ 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 $E_{\phi }$ into generalized irreversible CHP and performing multi-objective optimizations with 15 objective combinations considering four performance indicators.