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Register a new userThermal optimization of Curzon-Ahlborn heat engines operating under some generalized efficient power regimes
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Added by
L. A. Arias-Hernandez
Publication date
2018
fields
Physics
and research's language is
English
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In order to establish better performance compromises between the process functionals of a heat engine, in the context of finite time thermodynamics (FTT), we propose some generalizations for the well known Efficient Power function through certain variables called <<Generalization Parameters>>. These generalization proposals show advantages in the characterization of operation modes for an endoreversible heat engine model. In particular, with introduce the k-Efficient Power regime. For this objective function we find the performance of the operation of some power plants through the parameter k. Likewise, for plants that operate in a low efficiency zone, within a configuration space, the k parameter allow us to generate conditions for these plants to operate inside of a high efficiency and low dissipation zone.
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The Curzon-Ahlborn (CA) efficiency, as the efficiency at the maximum power (EMP) of the endoreversible Carnot engine, has significant impact in finite-time thermodynamics. In the past two decades, a lot of efforts have been made to seek a microscopic theory of the CA efficiency. It is generally believed that the CA efficiency is approached in the symmetric low-dissipation regime of dynamical models. Contrary to the general belief, without the low-dissipation assumption, we formulate a microscopic theory of the CA engine realized with an underdamped Brownian particle in a class of non-harmonic potentials. This microscopic theory not only explains the dynamical origin of all assumptions made by Curzon and Ahlborn, but also confirms that in the highly underdamped regime, the CA efficiency is always the EMP irrespective of the symmetry of the dissipation. The low-dissipation regime is included in the microscopic theory as a special case. Also, based on this theory, we obtain the control scheme associated with the maximum power for any given efficiency, as well as analytical expressions of the power and the efficiency statistics for the Brownian CA engine. Our research brings new perspectives to experimental study of finite-time microscopic heat engines featured with fluctuations.
A specific class of stochastic heat engines driven cyclically by time-dependent potential, which is defined in the half-line ($0<x<+infty$), is analysed. For such engines, most of their physical quantities can be obtained explicitly, including the entropy and internal energy of the heat engine, as well as output work (power) and heat exchange with the environment during a finite time interval. The optimisation method based on the external potential to reduce {it irreversible} work and increase energy efficiency is presented. With this optimised potential, efficiency $eta^*$ and its particular value at maximum power $eta^*_{rm EMP}$ are calculated and discussed briefly.
We consider the performance of periodically driven stochastic heat engines in the linear response regime. Reaching the theoretical bounds for efficiency and efficiency at maximum power typically requires full control over the design and the driving of the system. We develop a framework which allows to quantify the role that limited control over the system has on the performance. Specifically, we show that optimizing the driving entering the work extraction for a given temperature protocol leads to a universal, one-parameter dependence for both maximum efficiency and maximum power as a function of efficiency. In particular, we show that reaching Carnot efficiency (and, hence, Curzon-Ahlborn efficiency at maximum power) requires to have control over the amplitude of the full Hamiltonian of the system. Since the kinetic energy cannot be controlled by an external parameter, heat engines based on underdamped dynamics can typically not reach Carnot efficiency. We illustrate our general theory with a paradigmatic case study of a heat engine consisting of an underdamped charged particle in a modulated two-dimensional harmonic trap in the presence of a magnetic field.
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.
The efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill such gap with a stepwise Carnot-like cycle, which consists the discrete isothermal process (DIP) and adiabatic process. With DIP, we validate the widely adopted assumption of mathscr{C}/t relation of the irreversible entropy generation S^{(mathrm{ir})}, and show the explicit dependence of the coefficient mathscr{C} on the fluctuation of the speed of tuning energy levels as well as the microscopic coupling constants to the heat baths. Such dependence allows to control the irreversible entropy generation by choosing specific control schemes. We further demonstrate the achievable efficiency at maximum power and the corresponding control scheme with the simple two-level system. Our current work opens new avenues for the experimental test, which was not feasible due to the lack the of the practical control scheme in the previous low-dissipation model or its equivalents.
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