Optimization, Stability, and Entropy in Endoreversible Heat Engines

Abstract

The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that the system has a stationary fixed point, along with a Taylor expansion in the first order of the input/output heat fluxes, without further specifications regarding the properties of the working fluid or the heat device specifications. Specific cases of the Newton and the phenomenological heat transfer laws in a Carnot-like heat engine model were analyzed. It was shown that the evolution of the trajectories toward the stationary state have relevant consequences on the performance of the system. A major role was played by the symmetries/asymmetries of the conductance ratio σhc of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small σhc values, the thermodynamic trajectories evolved near the endoreversible limit, improving the efficiency and power output values with a decrease in entropy generation; (2) for large σhc values, the thermodynamic trajectories evolved either near the Pareto front or near the endoreversible limit, and in both cases, they improved the efficiency and power values with a decrease in entropy generation; (3) for the symmetric case (σhc=1), the trajectories evolved either with increasing entropy generation tending toward the Pareto front or with a decrease in entropy generation tending toward the endoreversible limit. Moreover, it was shown that the total entropy generation can define a time scale for both the operation cycle time and the relaxation characteristic time.

Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Diesel Cycle

“…Therefore, the MOO solution set is not unique, and a series of feasible alternatives can be obtained, which are called Pareto frontiers. In this section, , , , and are used as objective functions; the compression ratio ( ) is used as an optimization variable; and NSGA-II [ 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 ] is used to perform bi-, tri-, and quadru-objective optimizations for an irreversible Diesel cycle. Through three different solutions, that is, LINMAP, TOPSIS, and Shannon entropy, the optimization results under different objective function combinations are obtained.…”

“…Shi et al [ 44 ] and Ahmadi et al [ 45 ] performed MOO of the Atkinson cycle when the working fluid’s specific heats were constants [ 44 ] and varied with temperature non-linearly [ 45 ]. Gonzalez et al [ 46 ] performed MOO on , , and entropy generation of an endoreversible Carnot engine and analyzed the stability of the Pareto frontier. Ata et al [ 47 ] performed parameter optimization and sensitivity analysis for an organic Rankine cycle with a variable temperature heat source.…”

Optimization Modeling of Irreversible Carnot Engine from the Perspective of Combining Finite Speed and Finite Time Analysis

“…However, regarding the usefulness of the FTT, the endoreversible model has the merit of launching nowadays the competition of finding new upper bounds of thermal machines performance, closer to the real one. Thus, progress has been made in the modeling and optimization of thermodynamic processes and cycles [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ], with special attention to the common ones in thermal machines: Otto cycle [ 27 ], Stirling engine [ 28 ], Kalina cycle [ 30 ], and Brayton cycle [ 31 , 32 ]. The results obtained [ 30 , 31 ] have shown that besides the gains of FTT optimization with three or four objectives, the original results reported in the initial work of the FTT theory [ 3 , 4 , 5 ] are also revealed.…”

Performance Analysis and Four-Objective Optimization of an Irreversible Rectangular Cycle

“…After decades of development, a series of instructive and practical achievements have been obtained in finite time thermodynamics [1][2][3][4][5][6][7][8], the research objects of which include heat engines [9][10][11][12][13][14][15], refrigerators [16,17], heat pumps [18], chemical cycles [19], and quantum cycles [20,21]. The rectangular cycle (RC) is composed of four thermodynamic processes, its endothermic processes are closed to the endothermic processes of the dual cycle, and its exothermic processes are closed to the exothermic processes of the Miller cycle.…”