Global Stability Analysis of a Curzon–Ahlborn Heat Engine under Different Regimes of Performance

Reyes-Ramírez, Israel; Barranco-Jiménez, M. A.; Rojas-Pacheco, A.; Guzmán‐Vargas, L.

doi:10.3390/e16115796

Cited by 15 publications

(10 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…T hw = x and T cw = ȳ are known as internal working temperatures, and they define heat fluxes Qh = J h (from the internal heat deposit at temperature x to the system) and Qc = J c (from the system to the internal heat deposit at temperature ȳ). Hence, we use x, ȳ, Jh and Jc to specify temperatures and heat fluxes in a steady state [16,17,18,19,20,29,30]. As the endoreversibility hypothesis implies the internal entropy production is null [5,6,7,8,9,10], then:…”

Section: Steady States Of a Ca Heat Engine (Endoreversible Model)mentioning

confidence: 99%

“…All of the aforementioned studies have been focused on determining the relaxation times of the decaying rate to the stationary fixed points, assuming local perturbations around these values. On the other hand, Reyes-Ramírez et al [29,30] investigated the global stability of a CA heat engine operating at different performance regimes by means of the Lyapunov method. They found the Lyapunov function as a way to prove the asymptotic stability behavior of the intermediate temperatures around the steady state.…”

Section: Introductionmentioning

confidence: 99%

“…They found the Lyapunov function as a way to prove the asymptotic stability behavior of the intermediate temperatures around the steady state. In this work, following the procedure reported in [29,30], we study the local and global stability of the k-efficient power regime [15]. The paper is organized as follows: In Section 2, we present the main steady state characteristics of an endoreversible engine model (CA model) at maximum k-efficient power regime.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Local and global stability analysis of a Curzon-Ahlborn model applied to power plants working at maximum $k$-efficient power

Valencia-Ortega,

Levario-Medina,

Barranco-Jiménez

2020

Preprint

View full text Add to dashboard Cite

The analysis of the effect of noisy perturbations on real heat engines, working on any steady-state regime has been a topic of interest within the context of Finite-Time Thermodynamics (FTT). The study of their local stability has been proposed through the so-called performance regimes: maximum power output, maximum ecological function, among others. Recently, the global stability analysis of an endoreversible heat engine was also studied taking into account the same performance regimes. We present a study of local and global stability analysis of power plant models (the Curzon-Ahlborn model) operating on a generalized efficient power regime called maximum k-efficient power. We apply the Lyapunov stability theory to construct the Lyapunov functions to prove the asymptotically stable behavior of the steady-state of intermediate temperatures in the Curzon-Ahlborn model. We consider the effect of a linear heat transfer law on the phase portrait description of real power plants, as well as the role of the k parameter in the evolution of perturbations to heat flow. In general, restructured operation conditions show better stability in external perturbations.

show abstract

Section: Steady States Of a Ca Heat Engine (Endoreversible Model)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Local and global stability analysis of a Curzon-Ahlborn model applied to power plants working at maximum $k$-efficient power

Valencia-Ortega,

Levario-Medina,

Barranco-Jiménez

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…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%

Optimization, Stability, and Entropy in Endoreversible Heat Engines

González-Ayala

Roco

Medina

et al. 2020

Entropy

View full text Add to dashboard Cite

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.

show abstract

“…In this context, the combined cycle power plants in whose construction coexist two thermodynamic cycles from the same source of heat, have turned out to have a greater amount of available energy. Although in practice, the amount of non useful energy generated compared to the used one continues to be a big problem, it can be modulated (reduced) by paying attention to the operation regimes [10,11,12] with which this type of power plants can be operated. These regimes are normally associated with operation and design parameters that measure qualitatively the internal and external irreversibilities.…”

Section: Introductionmentioning

confidence: 99%

Energetic optimization considering a generalization of the ecological criterion in traditional simple-cycle and combined cycle power plants

Levario-Medina,

Valencia-Ortega,

Barranco-Jiménez

2020

Preprint

View full text Add to dashboard Cite

The fundamental issue in the energetic performance of power plants, working both as traditional fuel engines and as combined cycle turbine (gas-steam), lies in quantifying the internal irreversibilities which are associated with the working substance operating in cycles. Several irreversible models of energy converters have been studied under different contexts of non-equilibrium thermodynamics, their purpose is to find objective thermodynamic functions that determine more realistic bounds for real energy converters and at the same time reduce energy losses per cycle. As these objective functions characterize specific operation regimes, we focus our attention in one generalization of the so-called ecological function in terms of a generalizing parameter ( ) which can be related not only to a large number of accessible operation modes, but also to parameters representing both internal and external irreversibilities in models of power plants. In this work, we conclude the characteristic loops in the power output-efficiency space can be sketched, for either of the two irreversible heat engine models considered with heat leak. We found out that from a set of loops related to the physical constraints, the above systems work as heat engines and their operating conditions lie in 3 particular zones. The optimum zone featured by high power output and high efficiency is characterized through a relation between the irreversibility degrees and the constraints-parameters.

show abstract

Global Stability Analysis of a Curzon–Ahlborn Heat Engine under Different Regimes of Performance

Cited by 15 publications

References 21 publications

Local and global stability analysis of a Curzon-Ahlborn model applied to power plants working at maximum $k$-efficient power

Local and global stability analysis of a Curzon-Ahlborn model applied to power plants working at maximum $k$-efficient power

Optimization, Stability, and Entropy in Endoreversible Heat Engines

Energetic optimization considering a generalization of the ecological criterion in traditional simple-cycle and combined cycle power plants

Contact Info

Product

Resources

About