Research

10 pages, 400 KiB

Open AccessFeature PaperArticle

Improved Chambadal Model with New Optimization Results

by Michel Feidt and Monica Costea

Entropy 2024, 26(2), 125; https://doi.org/10.3390/e26020125 - 31 Jan 2024

Viewed by 534

This paper presents a continuation of the Chambadal model optimization of the irreversible Carnot engine. We retrieved the results presented in the Special Issue “Carnot Cycle and Heat Engine Fundamentals and Applications II” and enriched them with new contributions that allowed comparing two [...] Read more.

This paper presents a continuation of the Chambadal model optimization of the irreversible Carnot engine. We retrieved the results presented in the Special Issue “Carnot Cycle and Heat Engine Fundamentals and Applications II” and enriched them with new contributions that allowed comparing two points of view: (1) the now classical one, centered on entropy production in the four processes of the cycle, which introduces the action of entropy production, with several sequential optimizations; (2) the new one that is relative to an energy degradation approach. The same démarche of sequential optimization was used, but the results were slightly different. We estimate that the second approach is more representative of physics by emphasizing the energy conservation and the existence on an upper and a lower bound in the mechanical energy and power output of the engine. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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11 pages, 374 KiB

Open AccessArticle

Optimization Criteria and Efficiency of a Thermoelectric Generator

by V. H. Juárez-Huerta, N. Sánchez-Salas and J. C. Chimal-Eguía

Entropy 2022, 24(12), 1812; https://doi.org/10.3390/e24121812 - 13 Dec 2022

Cited by 2 | Viewed by 1815

Abstract

The efficiency of a thermoelectric generator model under maximum conditions is presented for two optimization criteria proposed under the context of finite-time thermodynamics, namely, the efficient power criterion and the Omega function, where this last function represents a trade-off between useful and lost [...] Read more.

The efficiency of a thermoelectric generator model under maximum conditions is presented for two optimization criteria proposed under the context of finite-time thermodynamics, namely, the efficient power criterion and the Omega function, where this last function represents a trade-off between useful and lost energy. The results are compared with the performance of the device at maximum power output. A macroscopic thermoelectric generator (TEG) model with three possible sources of irreversibilities is considered:

(i)

the electric resistance R for the Joule heating,

(i i)

the thermal conductances

K_{h}

and

K_{c}

of the heat exchangers between the thermal baths and the TEG, and

(i i i)

the internal thermal conductance K for heat leakage. In particular, two configurations of the macroscopic TEG are studied: the so-called exoreversible case and the endoreversible limit. It shows that for both TEG configurations, the efficiency at maximum Omega function is always greater than that obtained in conditions of maximum efficient power, and this in turn is greater than that of the maximum power regime. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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11 pages, 2551 KiB

Open AccessArticle

Global Stability of the Curzon-Ahlborn Engine with a Working Substance That Satisfies the van der Waals Equation of State

by Juan Carlos Pacheco-Paez, Juan Carlos Chimal-Eguía, Ricardo Páez-Hernández and Delfino Ladino-Luna

Entropy 2022, 24(11), 1655; https://doi.org/10.3390/e24111655 - 14 Nov 2022

Viewed by 1359

Abstract

In this paper, we show an analysis of the global stability of a Curzon–Ahlborn engine considering that the working substance of the engine satisfies the Van der Waals equation of state, which is more general than the ideal gas case. We use the [...] Read more.

In this paper, we show an analysis of the global stability of a Curzon–Ahlborn engine considering that the working substance of the engine satisfies the Van der Waals equation of state, which is more general than the ideal gas case. We use the Lyapunov stability theory for the case where the engine operates at a maximum power output. We analyze the steady state of the intermediate temperatures as well as the asymptotic behavior of the performance of the engine. Additionally, we study the relationship between the inherent time delay by analyzing the dynamic properties of the system and the stability of the steady state. We present illustrative graphs of the obtained results. Finally, we include a brief discussion of the obtained results and appropriate conclusions. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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18 pages, 4208 KiB

Open AccessArticle

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

by Haoran Xu, Lingen Chen, Yanlin Ge and Huijun Feng

Entropy 2022, 24(10), 1491; https://doi.org/10.3390/e24101491 - 19 Oct 2022

Cited by 4 | Viewed by 1250

Abstract

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 [...] Read more.

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

{\bar{P}}_{s}

, braking thermal efficiency

η_{s}

, dimensionless efficient power

{\bar{E}}_{p}

and dimensionless power density

{\bar{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

D

s reached for single-objective optimizations at maximum

{\bar{P}}_{s}

,

η_{s}

,

{\bar{E}}_{p}

, and

{\bar{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. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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26 pages, 5428 KiB

Open AccessArticle

Four-Objective Optimization of an Irreversible Magnetohydrodynamic Cycle

by Qingkun Wu, Lingen Chen, Yanlin Ge and Huijun Feng

Entropy 2022, 24(10), 1470; https://doi.org/10.3390/e24101470 - 14 Oct 2022

Cited by 6 | Viewed by 1007

Abstract

Based on the existing model of an irreversible magnetohydrodynamic cycle, this paper uses finite time thermodynamic theory and multi-objective genetic algorithm (NSGA-II), introduces heat exchanger thermal conductance distribution and isentropic temperature ratio of working fluid as optimization variables, and takes power output, efficiency, [...] Read more.

Based on the existing model of an irreversible magnetohydrodynamic cycle, this paper uses finite time thermodynamic theory and multi-objective genetic algorithm (NSGA-II), introduces heat exchanger thermal conductance distribution and isentropic temperature ratio of working fluid as optimization variables, and takes power output, efficiency, ecological function, and power density as objective functions to carry out multi-objective optimization with different objective function combinations, and contrast optimization results with three decision-making approaches of LINMAP, TOPSIS, and Shannon Entropy. The results indicate that in the condition of constant gas velocity, deviation indexes are 0.1764 acquired by LINMAP and TOPSIS approaches when four-objective optimization is performed, which is less than that (0.1940) of the Shannon Entropy approach and those (0.3560, 0.7693, 0.2599, 0.1940) for four single-objective optimizations of maximum power output, efficiency, ecological function, and power density, respectively. In the condition of constant Mach number, deviation indexes are 0.1767 acquired by LINMAP and TOPSIS when four-objective optimization is performed, which is less than that (0.1950) of the Shannon Entropy approach and those (0.3600, 0.7630, 0.2637, 0.1949) for four single-objective optimizations, respectively. This indicates that the multi-objective optimization result is preferable to any single-objective optimization result. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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11 pages, 1155 KiB

Open AccessArticle

Maximum Profit Output Configuration of Multi-Reservoir Resource Exchange Intermediary

by Lingen Chen and Shaojun Xia

Entropy 2022, 24(10), 1451; https://doi.org/10.3390/e24101451 - 11 Oct 2022

Cited by 2 | Viewed by 898

Abstract

A model of a multi-reservoir resource exchange intermediary also defined as a commercial engine is proposed according to analogies and similarities between thermodynamics and economics. The optimal configuration of a multi-reservoir commercial engine with a maximum profit output objective is determined by applying [...] Read more.

A model of a multi-reservoir resource exchange intermediary also defined as a commercial engine is proposed according to analogies and similarities between thermodynamics and economics. The optimal configuration of a multi-reservoir commercial engine with a maximum profit output objective is determined by applying optimal control theory. The optimal configuration consists of two instantaneous constant commodity flux processes and two constant price processes, and the configuration is independent of a number of economic subsystems and commodity transfer law qualitatively. The maximum profit output needs some economic subsystems to never contact with the commercial engine during commodity transfer processes. Numerical examples are provided for a three-economic-subsystem commercial engine with linear commodity transfer law. The effects of price changes of an intermediate economic subsystem on the optimal configuration of a three-economic-subsystem and the performance of optimal configuration are discussed. The research object is general, and the results can provide some theoretical guidelines for operations of actual economic processes and systems. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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18 pages, 3903 KiB

Open AccessArticle

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

by Jinhu He, Lingen Chen, Yanlin Ge, Shuangshuang Shi and Fang Li

Entropy 2022, 24(10), 1445; https://doi.org/10.3390/e24101445 - 11 Oct 2022

Cited by 7 | Viewed by 1121

Abstract

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 (

\bar{R}

), coefficient of performance (

ε

[...] Read more.

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 (

\bar{R}

), coefficient of performance (

ε

), ecological function (

\bar{E C O}

), and figure of merit (

\bar{χ}

) of the ESER are taken as objective functions. Energy boundary

(E^{'} / k_{B})

and resonance width

(Δ E / k_{B})

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^{'} / k_{B}

and

Δ E / k_{B}

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 (

\bar{E C O} - \bar{R} - ε - \bar{χ}

), while the deviation indices are 0.1085, 0.8455, 0.1865, and 0.1780 for four single-objective optimizations of maximum

\bar{E C O}

,

\bar{R}

,

ε

, and

\bar{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^{'} / k_{B}

and

Δ E / k_{B}

range mainly from 12 to 13, and 1.5 to 2.5, respectively, for the four-objective optimization. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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20 pages, 5409 KiB

Open AccessArticle

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

by Lei Tian, Lingen Chen, Yanlin Ge and Shuangshuang Shi

Entropy 2022, 24(10), 1443; https://doi.org/10.3390/e24101443 - 10 Oct 2022

Cited by 14 | Viewed by 1377

Abstract

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 [...] Read more.

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

0.308 W

to

0.2381 W

. When the total heat exchanger area is increased from

0.03 m^{2}

to

0.09 m^{2}

, the maximum efficient power is increased from

0.0603 W

to

0.3777 W

. 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. Full article

(This article belongs to the Special Issue Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT))

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