Endoreversible Carnot Heat Engine Research Articles

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.

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.

Output power analyses of an endoreversible Carnot heat engine with irreversible heat transfer processes based on generalized heat transfer law**Project supported by the Youth Programs of Chongqing Three Gorges University, China (Grant No. 13QN18).

In this paper, an endoreversible Carnot heat engine with irreversible heat transfer processes is analyzed based on generalized heat transfer law. The applicability of the entropy generation minimization, exergy analyses method, and entransy theory to the analyses is discussed. Three numerical cases are presented. It is shown that the results obtained from the entransy theory are different from those from the entropy generation minimization, which is equivalent to the exergy analyses method. For the first case in which the application preconditions of the entropy generation minimization and entransy loss maximization are satisfied, both smaller entropy generation rate and larger entransy loss rate lead to larger output power. For the second and third cases in which the preconditions are not satisfied, the entropy generation minimization does not lead to the maximum output power, while larger entransy loss rate still leads to larger output power in the third case. For the discussed cases, the concept of entransy dissipation is not applicable for the analyses of output power. The problems in the negative comments on the entransy theory are pointed out and discussed. The related researchers are advised to focus on some new specific application cases to show if the entransy theory is the same as some other theories.

Progress in the study on finite time thermodynamic optimization for direct and reverse two-heat-reservoir thermodynamic cycles

The results obtained by using finite time thermodynamics (FTT) are universal and have become one of important foundations of thermo-physics. A large number of researches have been carried out in the performance optimizations and optimal configurations of single-and multi-stage two-heat-reservoir direct and inverse thermodynamic cycles by using FTT. The obtained new results have more important practical significance for engineering design and optimization than those obtained by using classical thermodynamics. This paper reviews the new advances of the optimal performances and optimal configurations of single and multi-stage two-heat-reservoir direct and inverse thermodynamic cycles following different heat transfer laws, including the new advances of the optimal performances of endoreversible and irreversible Carnot heat engine, Carnot refrigerator and Carnot heat pump cycles under different heat transfer laws, and the new advances of the optimal configurations of two-heat-reservoir heat engine, refrigerator and heat pump cycles, as well as multi-stage complex thermodynamic cycles with different heat transfer laws.

Hamilton-Jacobi-Bellman equations and dynamic programming for power-optimization of a multistage heat engine system with generalized convective heat transfer law

A multistage endoreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convective heat transfer law [q∝(ΔT)m] is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations, which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid. Based on the universal optimization results, the analytical solution for the Newtonian heat transfer law (m=1) is also obtained. Since there are no analytical solutions for the other heat transfer laws (m≠1), the continuous HJB equations are discretized and dynamic programming algorithm is performed to obtain the complete numerical solutions of the optimization problem. The relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail. The results obtained provide some theoretical guidelines for the optimal design and operation of practical energy conversion systems.

Ecological performance of an endoreversible Carnot heat engine with complex heat transfer law

The optimal ecological performance of an endoreversible Carnot engine, in which the transfer between the working fluid and the heat reservoirs obeys a complex heat transfer law, including generalized convective heat transfer law and generalized radiative heat transfer law, Q∝ (Δ T n ) m , is derived by taking into account an ecological optimization criterion as the objective function, which consists of maximizing a function representing the best compromise between the power output and entropy generation rate of the heat engine. The obtained results include the optimal ecological performance of the endoreversible Carnot heat engine with various heat transfer laws obtained in many studies.

Performance analysis of endoreversible combined Carnot cycles based on new maximum efficient power (MEP) approach

The efficient power, defined as the product of power output and efficiency of the engine, is taken as the objective for performance analysis and optimization of an endoreversible combined Carnot heat engine model in the viewpoint of finite time thermodynamics (FTT) or entropy generation minimization (EGM). The effects of finite-rate heat transfer, cycle temperature ratio and thermal-conduction parameters are considered in the analysis. The obtained results are compared with those obtained using maximum power (MP) and maximum power density (MPD) criterion. The design parameters for the optimal performances were derived analytically, and the effects of cycle temperature ratio and thermal conductance on it are investigated. The engines designed at MEP approach are more efficient and smaller than those designed at MP and MPD conditions. Copyright The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

Power versus efficiency characteristic of an endoreversible Carnot heat engine with heat transfer law q α (Δ Tn)m

SYNOPSIS The relationship between optimal power output and efficiency of an endoreversible Carnot heat engine is derived based on a new generalised heat transfer law, including a generalised convective heat transfer law and a generalised radiative heat transfer law, q ∞ (ΔTn)m The results include those obtained in many references and can provide some theoretical guidance for the design of practical heat engines.

A comparative performance analysis of an endoreversible heat engine with thermal reservoir of finite heat capacitance under maximum power density and maximum power conditions

SYNOPSIS This paper presents a finite time thermodynamic optimisation based on maximum power density criterion for an endoreversible Carnot heat engine model coupled to variable temperature heat reservoirs. Expressions for the power density and optimal efficiency at maximum power density conditions are derived with heat resistance losses in the hot and cold side heat exchangers. The results obtained are compared with those using the maximum power criterion. The influences of some design parameters on the maximum power density are provided by numerical examples, and the advantages and disadvantages of maximum power density are analysed. Power plant design for maximum power density leads to higher efficiency and smaller size.

Finite time thermodynamic analysis of endoreversible Stirling heat engine with regenerative losses

This communication presents an investigation of a finite time thermodynamic analysis of an endoreversible Stirling heat engine. Finite time thermodynamics has been applied to maximize the power output and the corresponding thermal efficiency of an endoreversible Stirling heat engine with internal heat loss in the regenerator and for the finite heat capacity of the external reservoirs. The effect of the effectiveness of the various heat exchangers, the inlet temperatures of external heat reservoirs on the power output and the corresponding thermal efficiency have been studied. It is seen that an endoreversible Stirling heat engine with an ideal regenerator ( ϵ R=1.00) is as efficient as an endoreversible Carnot heat engine. It is also found that the maximum power output increases with the heat capacitance rates and effectiveness of the source/sink side heat exchangers while thermal efficiency increases with the effectiveness of the regenerator.

Finite time thermodynamic evaluation of irreversible Ericsson and Stirling heat engines

This paper presents an investigation on finite time thermodynamic evaluation of Ericsson and Stirling heat engines. Finite time thermodynamics has been applied to optimise the power output and thermal efficiency of both engines, including finite heat capacitance rates of the heat source and sink reservoirs external fluids, finite time heat transfer, regenerative heat losses and direct heat leak losses from source to sink reservoirs. The presence of these effects causes irreversibilities and affects the performance of the Ericsson and Stirling heat engines using ideal or real gas as the working fluid/substance. It is found that both cycles with an ideal regenerator ( ϵ R=1.00) are as efficient as an endoreversible Carnot heat engine operating at the same conditions, but this is not practical because an ideal regenerator requires either infinite regenerator area or infinite regeneration time. It is also found that the regenerative heat losses, regenerator effectiveness and the direct heat leak losses do not affect the maximum power output of either heat engine. Some special cases are also described.

Comment on “A universal optimum work rate potential for continuous endoreversible Carnot heat engine cycles” [J. Appl. Phys. 80, 3619 (1996)

It is pointed out that there is not a certain universal relation for the power outputs of continuous endoreversible and reversible Carnot heat engine cycles operating between the same temperature limits, and the relevant conclusion obtained by Blank and Bhattacharyya in a recent article of this journal is incorrect.

Equivalent combined cycle of an endoreversible absorption heat transformer and optimal analysis of primary performance parameters

With the help of a combined cycle model having an endoreversible Carnot heat pump driven by an endoreversible Carnot heat engine, the optimal performance of an absorption heat transformer affected by the irreversibility of finite-rate heat transfer is investigated. The maximum specific heating load of the heat transformer and the corresponding coefficient of performance are derived. It is proven that the state of the maximum specific heating load of the endoreversible heat transformer corresponds to that of the maximum specific power output of the endoreversible Carnot heat engine in the combined cycle model. A detailed analysis of the optimal distribution of heat exchanger areas is given. Other problems concerning the optimal design of absorption heat transformers are also discussed.

Maximum power density for an endoreversible carnot heat engine

An analysis using maximum power-density criteria has been carried out for an endoreversible Carnot heat engine. The results have been compared with known results on maximum power analysis. The design parameters at maximum power density lead to smaller and more efficient endoreversible Carnot heat engines than those working at maximum power output.

96/06754 Experimental study of turbulent flow in the near wakes of single and tandem prisms

With the help of a combined cycle model having an endoreversible Carnot heat pump driven by an endoreversible Carnot heat engine, the optimal performance of an absorption heat transformer affected by the irreversibility of finite-rate heat transfer is investigated. The maximum specific heating load of the heat transformer and the corresponding coefficient of performance are derived. It is proven that the state of the maximum specific heating load of the endoreversible heat transformer corresponds to that of the maximum specific power output of the endoreversible Carnot heat engine in the combined cycle model. A detailed analysis of the optimal distribution of heat exchanger areas is given. Other problems concerning the optimal design of absorption heat transformers are also discussed.

A universal optimum work rate potential for continuous endoreversible Carnot heat engine cycles

The theory of finite-time thermodynamics for continuous endoreversible cycles gives rise to an optimum efficiency at maximum power output of η=1−(TL/TH)0.5 in contrast to the upper limit of η=1−(TL/TH) obtained from infinite-time thermodynamics. It is shown here that, additionally, for continuous Carnot cycles, the finite-time optimum rate of work output (Ẇopt), is exactly half of that obtained for infinite-time reversible cycles (Carnot work rate, Ẇrev) operating between the same temperature limits (i.e. Ẇopt=1/2Ẇrev). This expression is true for both unoptimized as well as optimized mass flow rate conditions. The formulation used in the analysis is universal for all working substances for cycles using linear heat transfer laws.

The maximum power output and maximum efficiency of an irreversible Carnot heat engine

The effect of thermal resistance, heat leakage and internal irreversibility resulting from the working fluid on the performance of a Carnot heat engine is investigated using a new cyclic model. The power output and efficiency of the heat engine are adopted as objective functions for heat engine optimization. The optimal performance of the heat engine is analysed systematically. Some significant results are obtained. For example, the maximum power output and maximum efficiency are determined. The efficiency of the heat engine at maximum power output and the power output of the heat engine at maximum efficiency are also calculated. Curves of the power output varying with the efficiency of the heat engine are obtained. These curves can indicate clearly the rational regions of efficiency and power output for an irreversible Carnot heat engine. It is pointed out that all the conclusions concerning a reversible Carnot heat engine, an endoreversible Carnot heat engine only affected by thermal resistance and an irreversible Carnot heat engine with internal irreversibility and/or heat leakage can be deduced from the results in this paper.

Finite-time optimizations of a heat engine

We study the power and efficiency of a finite-time heat engine. We consider an endoreversible Carnot heat engine coupled to heating and cooling fluids and determine the maximum power output and efficiency to obtain a bound on the power-conversion systems. While the maximum power and the operating temperatures of the heat engine are functions of the heat-reservoir temperatures, heat-reservoir capacity rates and heat-transfer rates, the efficiency at maximum power depends primarily on the initial temperatures of the heating and cooling fluids. The efficiency at maximum power provides a measure of the power available in a practical heat engine.