Local Stability of Curzon-Ahlborn Cycle with Non-Linear Heat Transfer for Maximum Power Output Regime

Ladino-Luna, Delfino; Portillo-Díaz, Pedro; Páez-Hernández, Ricardo T.

doi:10.4236/jmp.2013.47a2004

Cited by 4 publications

(5 citation statements)

References 20 publications

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“…Especially when the thermalization mechanisms are fast enough compared to the cycle time in agreement with local equilibrium. This allows to incorporate, in a straightforward way, stochastic-type perturbations into the analysis through additive noise in Equation (14).…”

Section: Discussionmentioning

confidence: 99%

“…The magnitudes of the relaxation times t 1 = −1/λ 1 and t 2 = −1/λ 2 are obtained from the eigenvalues, λ 1,2 , of the square matrix in the right-hand side of Equation (14). For the cases k = 1 and k = −1, they are:…”

Section: Stability Dynamics and Relaxation Timesmentioning

confidence: 99%

“…Especially in the realm of finite-time thermodynamics, endoreversible and irreversible models have, in their assets, a good number of works in this regard. From the pioneering work of Santillan et al [10], a number of studies have analyzed the local and global stability of a variety of operation regimes [11][12][13][14][15][16][17][18], including economic factors [19], and have extended the analysis to heat pumps, refrigerators, and generalized heat engines [17,[20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Optimization, Stability, and Entropy in Endoreversible Heat Engines

González-Ayala

Roco

Medina

et al. 2020

Entropy

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Stability Dynamics and Relaxation Timesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization, Stability, and Entropy in Endoreversible Heat Engines

González-Ayala

Roco

Medina

et al. 2020

Entropy

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“…Como se puede observar en la literatura, se han realizado diversos estudios sobre el desempeño de dispositivos convertidores de energía a partir de la hipótesis de transferencia calor en un tiempo finito. Particularmente se han estudiado diversos criterios de desempeño del ciclo de Curzon-Ahlborn (Gutkowicz et al, 1978;Rubin, 1980;Angulo-Brown, 1991); se ha aplicado a ciclos que modelan máquinas reales (Mozurkevich, 1982;Angulo-Brown et al, 1994;Lefft, 1987); se ha usado en el análisis de sistemas en estado estable (Santillán et al, 2001;Ladino-Luna et al, 2013;Páez-Hernández et al, 2018); y se han propuesto simplificaciones de los parámetros variables del ciclo de Curzon-Ahlborn (Agrawal, 2009;Páez-Hernández et al, 2016); entre otros muchos tópicos y autores. Además, con esa misma hipótesis (transferencia calor en un tiempo finito) se ha abordado recientemente un estudio de ciclos para máquinas térmicas como un modelo realista de la máquina Stirling (Lanzetta et al, 2016), una nueva optimización del ciclo Diesel (Zhu et al, 2019), un estudio de plantas hibridas solares (Merchán et al, 2020), entre muchos otros tópicos.…”

Section: Introductionunclassified

El ciclo Zilch en el contexto de la termodinámica de tiempos finitos: eficiencia y potencia de salida

2021

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El principal objetivo del presente estudio es examinar el ciclo Zilch desde el punto de vista de la termodinámica de tiempos finitos. Se propone una modificación del ciclo original, incluyendo explícitamente la diferencia entre temperaturas de trabajo y temperaturas de las fuentes de calor. Se construyen las expresiones de potencia de salida y eficiencia del ciclo con ciertas variables neutras, definidas como razones entre temperaturas de trabajo y de las fuentes. Se establecen restricciones para simplificar las expresiones obtenidas de potencia y eficiencia, y se imponen restricciones apropiadas para hallar sus regiones de existencia física. Los resultados muestran la viabilidad de los procedimientos usados, y la posibilidad que el ciclo estudiado sirva como modelo teórico para representar una planta con regeneración de calor. Se concluye que es posible describir el comportamiento de una máquina o planta de poder a través de la descripción del comportamiento de la potencia y la eficiencia.

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“…Since then, the stability of different types of endoreversible engines has been studied. Not only their performance in a variety of operating regimes has been tackled [4][5][6][7][8], but also economic improvements have been discussed [9][10][11]. The stability of heat pumps, refrigerators, and generalized heat engines has been analyzed as well [8,[12][13][14][15][16][17][18][19][20][21], complementing other possibilities, all of them within the endoreversible framework.…”

Section: Introductionmentioning

confidence: 99%

Local-stability analysis of a low-dissipation heat engine working at maximum power output

et al. 2017

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In this paper we address the stability of a low-dissipation (LD) heat engine (HE) under maximum power conditions. The LD system dynamics are analyzed in terms of the contact times between the engine and the external heat reservoirs, which determine the amount of heat exchanged by the system. We study two different scenarios that secure the existence of a single stable steady state. In these scenarios, contact times dynamics are governed by restitutive forces that are linear functions of either the heat amounts exchanged per cycle, or the corresponding heat fluxes. In the first case, according to our results, preferably locating the system irreversibility sources at the hot-reservoir coupling improves the system stability and increases its efficiency. On the other hand, reducing the thermal gradient increases the system efficiency but deteriorates its stability properties, because the restitutive forces are smaller. Additionally, it is possible to compare the relaxation times with the total cycle time and obtain some constraints upon the system dynamics. In the second case, where the restitutive forces are assumed to be linear functions of the heat fluxes, we find that although the partial contact time presents a locally stable stationary value, the total cycle time does not; instead, there exists an infinite collection of steady values located in the neighborhood of the fixed point, along a one-dimensional manifold. Finally, the role of dissipation asymmetries on the efficiency, the stability, and the ratio of the total cycle time to the relaxation time is emphasized.

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Local Stability of Curzon-Ahlborn Cycle with Non-Linear Heat Transfer for Maximum Power Output Regime

Cited by 4 publications

References 20 publications

Optimization, Stability, and Entropy in Endoreversible Heat Engines

Optimization, Stability, and Entropy in Endoreversible Heat Engines

El ciclo Zilch en el contexto de la termodinámica de tiempos finitos: eficiencia y potencia de salida

Local-stability analysis of a low-dissipation heat engine working at maximum power output

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