Endoreversible Heat Engine Research Articles

Non-unique detailed constructions of Curzon-Ahlborn cycle on thermodynamic plane

The Curzon-Ahlborn (CA) cycle is a paradigmatic model of endoreversible heat engines, which yields the so-called CA efficiency as the efficiency at maximum power. Due to the arbitrariness of the relationship between the steady temperature and the time taken for the isothermal process of the CA cycle, the constructions of the CA cycle on the thermodynamic plane are not unique. Here, we give some of the detailed constructions of the CA cycle on the thermodynamic plane, using an ideal gas as a working substance. It is shown that these constructions are equal to each other in the maximum power regime in the sense that they achieve the best trade-off between the work and the inverse cycle-time, known as the Pareto front in multi-objective optimization problems.

Performance enhancement of quantum Brayton engine via Bose-Einstein condensation.

Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.

Optimization analysis of an endoreversible quantum heat engine with efficient power function

Abstract We study the optimal performance of an endoreversible quantum dot heat engine, in which the heat transfer between the system and baths is mediated by qubits, operating under the conditions of a trade-off objective function known as the maximum efficient power function defined by the product of power and efficiency of the engine. First, we numerically study the optimization of the efficient power function for the engine under consideration. Then, we obtain some analytic results by applying a high-temperature limit and compare the performance of the engine at maximum efficient power function to the engine operating in the maximum power regime. We find that the engine operating at maximum efficient power function produces at least 88.89 % of the maximum power output while at the same time reducing the power loss due to entropy production by a considerable amount. We conclude by studying the stochastic simulations of the efficiency of the engine in maximum power and maximum efficient power regime. We find that the engine operating at maximum power is subjected to fewer power fluctuations as compared to the one operating at maximum efficient power function.

Performance optimization of solar‐powered heat engine using a multiobjective accelerated algorithm

AbstractIn this study, a multiobjective optimization approach was used to conduct a thermodynamic investigation of a solar Brayton and endoreversible heat engine. The thermo‐economic performance capabilities of such machines with hybrid input power, solar‐fuel, are examined numerically. Throughout this study, three performance indicators of the cycle, including the power output, the thermo‐economic performance function, and the thermal efficiency are optimized concurrently employing a multiobjective steepest descent method, named the Accelerated Diagonal Steepest Descent algorithm. Furthermore, to properly analyze the error, three strategies are employed in the decision‐making step to identify the optimal compromise solution, and the deviation indices under these strategies are analyzed. The numerical experiments reveal that the present algorithm outperforms the two popular multiobjective algorithms: the multiobjective particle swarm optimization method and the elitist nondominated sorting genetic algorithm. The relevance of the presented algorithm with respect to the previous ones is examined by means of a deviation index. Finally, these experiments show the optimal design parameters which lead to the best performance of the heat engine.

Multilayer Graphene as an Endoreversible Otto Engine.

We examine the performance of a finite-time, endoreversible Otto heat engine with a working medium of monolayer or multilayered graphene subjected to an external magnetic field. As the energy spectrum of multilayer graphene under an external magnetic field depends strongly on the number of layers, so too does its thermodynamic behavior. We show that this leads to a simple relationship between the engine efficiency and the number of layers of graphene in the working medium. Furthermore, we find that the efficiency at maximum power for bilayer and trilayer working mediums can exceed that of a classical endoreversible Otto cycle. Conversely, a working medium of monolayer graphene displays identical efficiency at maximum power to a classical working medium. These results demonstrate that layered graphene can be a useful material for the construction of efficient thermal machines for diverse quantum device applications.

Relation between fluctuations and efficiency at maximum power for small heat engines

We study the ratio between the variances of work output and heat input, $\eta^{(2)}$, for a class of four-stroke heat engines which covers various typical cycles. Recent studies on the upper and lower bounds of $\eta^{(2)}$ are based on the quasistatic limit and the linear response regime, respectively. We extend these relations to the finite-time regime within the endoreversible approximation. We consider the ratio $\eta_{\text{MP}}^{(2)}$ at maximum power and find that the square of the Curzon-Ahlborn efficiency, $\eta_{\text{CA}}^2$, gives a good estimate of $\eta_{\text{MP}}^{(2)}$ for the class of heat engines considered, i.e., $\eta_{\text{MP}}^{(2)} \simeq \eta_{\text{CA}}^2$. This resembles the situation where the Curzon-Ahlborn efficiency gives a good estimate of the efficiency at maximum power for various kinds of finite-time heat engines. Taking an overdamped Brownian particle in a harmonic potential as an example, we can realize such endoreversible small heat engines and give an expression of the cumulants of work output and heat input. The approximate relation $\eta_{\text{MP}}^{(2)} \simeq \eta_{\text{CA}}^2$ is verified by numerical simulations. This relation also suggests a trade-off between the efficiency and the stability of finite-time heat engines at maximum power.

Heat Engine Cycle Configurations for Maximum Work Output with Generalized Models of Reservoir Thermal Capacity and Heat Resistance

Abstract A class of two finite-heat-reservoir endoreversible heat engine with the generalized models of both the reservoir thermal capacities and heat resistances is investigated. The optimality condition for cycle maximum work output is derived by applying optimal control theory, and impacts of both thermal capacity characteristics of heat reservoirs and heat transfer laws on the optimal configurations are discussed. The results obtained in some previous researches are special cases of those obtained herein, which can provide some guidelines for optimal design of actual heat engines.

Assessment of the exergy and power density potential in the effluent flow of wastewater treatment plants

In this paper, historical data from the seven wastewater treatment plants in the Metropolitan Water Reclamation District of Greater Chicago (MWRDGC) is analyzed for its potential of waste heat recovery. The potential recovered waste heat is calculated monthly and yearly from effluent flow data and average regional minimum and maximum temperatures over a 10-year period between the years of 2011–2020. Based on the data analyzed, between 79.98 and 381.02 GWh/year could be recovered from all wastewater treatment plants in the MWRDGC combined. While the temperature differences between the effluent flow and the ambient temperature ranged between 0.3 and 19.2 °C, the primary factor in work energy potential was found to be the effluent mass flow rates, which ranged between 24,800 and 36,600 kg/s. Additionally, by viewing the work energy potential as the thermal source to either a theoretical Carnot heat engine or an endoreversible heat engine, a corresponding theoretical mechanical power output can be calculated. Despite Carnot and endoreversible thermal efficiencies of less than 5%, a power density between 0.004 and 2.84 W/m2 was calculated for every month except for June – August and was found to be comparable to hydropower generation systems.

Maximizing power output of endoreversible non-isothermal chemical engine via linear irreversible thermodynamics

Maximum power performance of an endoreversible non-isothermal chemical engine (NICE) with simultaneous heat and mass transfer is investigated in this paper. The heat and mass transfer processes are assumed to obey Onsager equations in linear irreversible thermodynamics. The power output of the endoreversible NICE as well as the corresponding vector efficiency [See Eq. (13) in this paper for its definition] are obtained analytically. Special cases for an endoreversible Carnot heat engine with the linear phenomenological heat transfer law [q∝Δ(T−1)] and an endoreversible isothermal chemical engine with the linear mass transfer law [g∝Δ(μ)] are further derived based on the general optimization results. Some numerical examples are provided, and the effects of changes of absorbed energy flux rate, mass flux rate, and heat and mass transfer phenomenological coefficients on the optimization results are analyzed. The results show that there are optimal absorbed energy flux rate and optimal mass flux rate for the power output of the endoreversible NICE to approach to its maximum; the relationship between the power output of the endoreversible NICE and its vector efficiency is paraboloid.

Local and global stability analysis of a Curzon–Ahlborn model applied to power plants working at maximum [formula omitted]-efficient power

The analysis of the effect of noisy perturbations on real heat engines working on the well-known steady-state regimes (maximum power output, maximum efficient power, etc.), has been a topic of interest within the context of Finite-Time Thermodynamics (FTT). In general, the small perturbation stability dynamics has been studied by considering some of the above-mentioned performance regimes. In this work, we intrinsically corroborate that the concepts of thermodynamic optimization and stability are not uncorrelated. On the other side, due to global stability dynamics opened an extension for the general study of thermal disturbances in endoreversible heat engines, we present a study of local and global stability analysis of a power plant model (the Curzon–Ahlborn model) operating on a generalized performance regime called k-efficient power. We also construct the Lyapunov functions to prove the global asymptotically stable behavior of this steady-state for the isothermal branches. In our study, we consider a Newtonian heat transfer law as well as the role of the k parameter in the evolution of perturbations to the heat fluxes. In general, the so-called restructured operation conditions show a better thermal stability dynamics than the original ones.

Concentrating solar thermal desalination: Performance limitation analysis and possible pathways for improvement

Solar thermal desalination is a viable approach for sustainable water production. Current thermal desalination technologies suffer from high specific energy consumption and energy mismatch. Concentrating solar collectors operate with high temperature energy and desalination systems operate with low temperature energy which leads to large exergy destruction. Herein, a thermodynamic model of an ideal concentrating solar-distillation process is developed to evaluate system integration and performance limitations (specific water production). Three different heating architectures are examined to understand how solar collector absorber temperature, concentration ratio, and recovery ratio impact system performance. A reversible solar distillation system operating with a concentration ratio of 10 at the optimal absorber temperature of 507 K can achieve a maximum specific water production of ~166.3 gs−1m−2 as the recovery ratio (rr) approaches zero. An endo-reversible heat engine model was formulated to consider system irreversibilities. Systems with irreversibilities (R = 0.001 K/kW or 0.005 K/kW) experience a decrease in the water production rate to 8.8 g s−1m−2 (rr = 51.4%) and 1.9 g s−1m−2 (rr = 65.2%). For efficient integration of solar collectors with thermal desalination systems, it is critical to adopt appropriate heating configurations and control absorber temperatures, system recovery ratio, and system irreversibilities.

Optimization, Stability, and Entropy in Endoreversible Heat Engines.

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 of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small 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 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 (), 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.

Applicability of the low-dissipation model: Carnot-like heat engines under Newton's law of cooling.

We investigate the validity of using the low-dissipation model (LD model) to describe the maximum power regime of the endoreversible model under Newton's law of cooling. We find it valid only when the temperature difference of heat reservoirs (T_{h}-T_{c},T_{h}>T_{c}) is small. Thus the efficiency at maximum power derived from the LD model is valid to the first order of Carnot efficiency when describing endoreversible heat engines. We conclude that the LD model produces the Curzon-Ahlborn efficiency (η_{CA}=1-sqrt[T_{h}/T_{c}]) in the maximum power regime with no dependence on dissipation ratios.

Optimal Power and Efficiency of Multi-Stage Endoreversible Quantum Carnot Heat Engine with Harmonic Oscillators at the Classical Limit.

At the classical limit, a multi-stage, endoreversible Carnot cycle model of quantum heat engine (QHE) working with non-interacting harmonic oscillators systems is established in this paper. A simplified combined cycle, where all sub-cycles work at maximum power output (MPO), is analyzed under two types of combined form: constraint of cycle period or constraint of interstage heat current. The expressions of power and the corresponding efficiency under two types of combined constrains are derived. A general combined cycle, in which all sub-cycles run at arbitrary state, is further investigated under two types of combined constrains. By introducing the Lagrangian function, the MPO of two-stage combined QHE with different intermediate temperatures is obtained, utilizing numerical calculation. The results show that, for the simplified combined cycle, the total power decreases and heat exchange from hot reservoir increases under two types of constrains with the increasing number (N) of stages. The efficiency of the combined cycle decreases under the constraints of the cycle period, but keeps constant under the constraint of interstage heat current. For the general combined cycle, three operating modes, including single heat engine mode at low “temperature” (SM1), double heat engine mode (DM) and single heat engine mode at high “temperature” (SM2), appear as intermediate temperature varies. For the constraint of cycle period, the MPO is obtained at the junction of DM mode and SM2 mode. For the constraint of interstage heat current, the MPO keeps constant during DM mode, in which the two sub-cycles compensate each other.

Quantum-dot heat engines with irreversible heat transfer

This work establishes a quantum heat engine considering qubits as the external heat transfer mediums. The authors find that the efficiency and the power output of the quantum heat engine are closely dependent on the microproperties of qubits, and consequently relate the irreversible heat transfer with quantum effects. The equivalent conditions between the quantum heat engines and the classical endoreversible Carnot heat engines are revealed

Performance of Feynman’s ratchet under a trade-off figure of merit: exact analysis versus estimation from prior information

We study the optimal performance of Feynman’s ratchet and pawl system operating as a heat engine (refrigerator), by optimizing the product of efficiency (coefficient of performance) and power output (cooling power), which is known as the efficient power (-criterion) in the literature. The analysis is performed by recourse to two different methods: the first employs an exact optimization over the internal energy scales of the device, and the second method is based on the use of prior information to estimate the optimal performance of the device. From the two-parameter optimization, universal features of the efficiency at maximum efficient power (EMEP) are shown. Then, an exact one-parameter optimization is carried out for the linear model of the engine in high temperature regime, by constraining one of the energy scales, and well-known forms of efficiency are obtained. Further, using the prior information approach, the obtained efficiency concurs with the EMEP of an endoreversible heat engine. An analogous analysis is carried out for the Feynman’s ratchet as a refrigerator. From the estimated behavior of the device under limited information, we are able to highlight universal features of its performance that remain robust under an inference analysis.

Thermal optimization of Curzon-Ahlborn heat engines operating under some generalized efficient power regimes

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.

Thermo-Economic Optimization of an Idealized Solar Tower Power Plant Combined with MED System.

Based on the reversible heat engine model, theoretical analysis is carried out for economic performance of a solar tower power plant (STPP) combined with multi-effect desalination (MED). Taking total revenue of the output power and the fresh water yield per unit investment cost as the economic objective function, the most economical working condition of the system is given by analyzing the influence of the system investment composition, the receiver operating temperature, the concentration ratio, the efficiency of the endoreversible heat engine, and the relative water price on the economic parameters of the system. The variation curves of the economic objective function are given out when the main parameter is changed. The results show that the ratio of water price to electricity price, or relative price index, has a significant impact on system economy. When the water price is relatively low, with the effect numbers of the desalination system increasing, and the economic efficiency of the overall system worsens. Only when the price of fresh water rises to a certain value does it make sense to increase the effect. Additionally, the threshold of the fresh water price to the electricity price ratio is 0.22. Under the conditions of the current price index and the heliostat (or reflector), the cost ratio and the system economy can be maximized by selecting the optimum receiver temperature, the endoreversible heat engine efficiency, and the optimum concentration ratio. Given the receiver surface temperature and the endoreversible heat engine efficiency, increasing the system concentration ratio of the heliostat will be in favor of the system economy.

Ecological efficiency of finite-time thermodynamics: A molecular dynamics study.

We present a molecular dynamics simulation of a two-dimensional Carnot engine. The optimization of this engine is achieved through the velocity of the piston, allowing not only the optimization of power output but also some other figures of merit involving entropy production. The maximum power and maximum ecological efficiencies are computed. It is shown that the near ideal gas working substance displays an endoreversible Carnot-like engine behavior. This can be considered as a prove of the validity of the Carnot-like endoreversible model. An effective reversible cycle different than the Carnot one is obtained, in agreement with theendoreversiblehypothesis flexibility. We compare the efficiencies stemming from an ideal gas approximation with those of the simulation, and then we propose a suitable approximation to an endoreversible heat engine and to a reversible Joule-Brayton cycle which fits very well to the simulation results. Finally, we show that the maximum ecological efficiency η=1-τ^{3/4}, which is also very close to the upper bound of the low-dissipation heat engine under maximum ecological (and Omega) conditions, is close for describing the dynamics of the simulated cycle under maximum power and maximum ecological conditions in the so-named heat engine operability region.

A Hybrid Electric and Thermal Solar Receiver

Summary Solar energy offers a promising renewable energy source; however, it is expensive to store electricity from photovoltaics (PV), the most widely deployed solar electricity technology. Solar thermal energy technologies can be paired with inexpensive thermal storage, but are more expensive overall. We have developed a solar receiver that combines PV and solar thermal systems to efficiently convert solar radiation to electricity (to be used immediately) and thermal energy (to be stored and converted to electricity on demand). This paper describes the Hybrid Electric And Thermal Solar (HEATS) receiver and models its performance. An idealized model predicts high solar-to-electricity efficiency (35.2%) with high dispatchability (44.2% of electricity from thermal energy) at an operating temperature of 775 K. Modeling using measured performance values for HEATS subcomponents predicts 26.8% efficiency and 81% dispatchability with silicon PV and 28.5% efficiency and 76% dispatchability with gallium arsenide PV, both operating at 700 K.