Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.     

Parametric optimum analysis of an irreversible Ericsson cryogenic refrigeration cycle working with an ideal Fermi gas

An irreversible model of an Ericsson cryogenic refrigeration cycle working with an ideal Fermi gas is established, which is composed of two isothermal and two isobaric processes. The influence of both the quantum degeneracy and the finite-rate heat transfer between the working fluid and the heat reservoirs on the performance of the cycle is investigated, based on the theory of statistical mechanics and thermodynamic properties of an ideal Fermi gas. The inherent regeneration losses of the cycle are analyzed. Expressions for several important performance parameters such as the coefficient of performance, cooling rate and power input are derived. By using numerical solutions, the cooling rate of the cycle is optimized for a given power input. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal regions of the coefficient of performance and power input are determined. Especially, the optimal performance of the cycle in the strong and weak gas degeneracy cases and the high temperature limit is discussed in detail. The analytic expressions of some optimized parameters are derived. Some optimum criteria are given. The distinctions and connections between the Ericsson refrigeration cycles working with the Fermi and classical gases are revealed.      

Performance analysis of a thermosize micro/nano heat engine

In a recent paper [A. Sisman, I. Muller, Phys. Lett. A 320 (2004) 360] the thermodynamic properties of ideal gases confined in a narrow box were examined theoretically. The so-called “thermosize effects” similar to thermoelectric effects, such as Seebeck-like thermosize effect, Peltier-like thermosize effect and Thomson-like thermosize effect, were analyzed. Like the thermoelectric generator, based on the thermosize effects we have established a model of micro/nano scaled ideal gas heat engine cycle which includes two isothermal and two isobaric processes. The expressions of power output and efficiency of this cycle in the two cases of reversible and irreversible heat exchange are derived and the optimal performance characteristics of the heat engine is discussed by some numerical example. The results obtained here will provide theoretical guidance for the design of micro/nano scaled device.     

Performance characteristics of low-dissipative generalized Carnot cycles with external leakage losses

Under the assumption of low-dissipation, a unified model of generalized Carnot cycles with external leakage losses is established. Analytical expressions for the power output and efficiency are derived. The general performance characteristics between the power output and the efficiency are revealed. The maximum power output and efficiency are calculated. The lower and upper bounds of the efficiency at the maximum power output are determined. The results obtained here are universal and can be directly used to reveal the performance characteristics of different Carnot cycles, such as Carnot heat engines, Carnot-like heat engines, flux flow engines, gravitational engines, chemical engines, two-level quantum engines,etc.     

工质变比热对不可逆Otto循环性能的影响

用有限时间热力学的方法分析空气标准Otto循环,由数值计算给出了存在不可逆损失和工质变比热时循环功率与压缩比、效率与压缩比以及功率和效率的特性关系,分析了工质变比热对不可逆Otto循环性能的影响特点,通过分析可知工质变比热特性对不可逆Otto循环性能有较大影响,在实际循环分析中应该予以考虑,本文所得结果对实际内燃机的设计有一定的指导意义。     

Modeling and Performance Optimization of an Irreversible Two-Stage Combined Thermal Brownian Heat Engine

Based on finite time thermodynamics, an irreversible combined thermal Brownian heat engine model is established in this paper. The model consists of two thermal Brownian heat engines which are operating in tandem with thermal contact with three heat reservoirs. The rates of heat transfer are finite between the heat engine and the reservoir. Considering the heat leakage and the losses caused by kinetic energy change of particles, the formulas of steady current, power output and efficiency are derived. The power output and efficiency of combined heat engine are smaller than that of single heat engine operating between reservoirs with same temperatures. When the potential filed is free from external load, the effects of asymmetry of the potential, barrier height and heat leakage on the performance of the combined heat engine are analyzed. When the potential field is free from external load, the effects of basic design parameters on the performance of the combined heat engine are analyzed. The optimal power and efficiency are obtained by optimizing the barrier heights of two heat engines. The optimal working regions are obtained. There is optimal temperature ratio which maximize the overall power output or efficiency. When the potential filed is subjected to external load, effect of external load is analyzed. The steady current decreases versus external load; the power output and efficiency are monotonically increasing versus external load.     

Combined cycles with gas turbine engines

Simple cycle gas turbine engines suffer from limited efficiencies and consequential dominance of fuel prices on generation costs. Combined cycles, however, exploit the waste heat from exhaust gases to boost power output, resulting in overall efficiencies around 50%, which are significantly above those of steam power plants. This paper reviews various types of combined cycles, including repowering, integrated gasification and other advanced systems.     

线性与非线性传热过程的Curzon-Ahlborn热机在任意功率时的效率

热机性能的优化是热力学领域的一个重要问题,而工质与热源之间的传热过程是热机工作时产生不可逆的主要来源.本文在引入功率增益和效率增益两个重要参数的基础上,基于一个简化的Curzon-Ahlborn热机模型并利用合比分比原理,给出了线性与非线性传热过程的热机在任意功率输出时的效率表达式,结合数值计算详细讨论了热机在任意功率输出时的特性.研究表明,参数ξ作为功率增益δP的函数存在两个分支:在第一分支上(不利情形),效率呈现出单调变化特征;在第二分支上(有利情形),效率随着的δP变化是非单调的且有最大值.随着传热指数的增加,热机的工作区域减小,这源于非线性传热过程包含热辐射所致.进一步发现功率-效率关系曲线存在权衡工作点,热机在该点附近工作能够实现最有效的热功转换.研究结果有助于深入理解具有不同传热过程热机的优化执行.     

Influence of quantum degeneracy on the performance of a gas Stirling engine cycle

Based on the state equation of an ideal quantum gas, the regenerative loss of a Stirling engine cycle working with an ideal quantum gas is calculated. Thermal efficiency of the cycle is derived. Furthermore, under the condition of quantum degeneracy, several special thermal efficiencies are discussed. Ratios of thermal efficiencies versus the temperature ratio and volume ratio of the cycle are made. It is found that the thermal efficiency of the cycle not only depends on high and low temperatures but also on maximum and minimum volumes. In a classical gas state the thermal efficiency of the cycle is equal to that of the Carnot cycle. In an ideal quantum gas state the thermal efficiency of the cycle is smaller than that of the Carnot cycle. This will be significant for deeper understanding of the gas Stirling engine cycle.     

Performance of a two-state quantum engine improved by the superposition effect

The performance of a two-state quantum engine under different conditions is analyzed.It is shown that the efficiency of the quantum engine can be enhanced by superposing the eigenstates at the beginning of the cycle.By employing the finite-time movement of the potential wall,the power output of the quantum engine as well as the efficiency at the maximum power output(EMP) can be obtained.A generalized potential is adopted to describe a class of two-level quantum engines in a unified way.The results obtained show clearly that the performances of these engines depend on the external potential,the geometric configuration of the quantum engines,and the superposition effect.Moreover,it is found that the superposition effect will enlarge the optimally operating region of quantum engines.     

能造出功率和效率都高的热机吗?——有限时间热力学的发展与展望

在热力学中,功率和效率是衡量热机性能的两个主要参数.根据经典热力学,可逆热机效率的上限是卡诺效率,但相应的功率为零.这是因为卡诺效率的实现依赖于时间无穷长的准静态假设.因此,如何根据实际需求,在保证热机功率前提下提高热机效率成为热力学一个重要的科学挑战问题.在20世纪上半叶应运而生的有限时间热力学,今天得到了蓬勃发展,...     

Optimization criteria of a Bose Brayton heat engine

An irreversible cycle model of the quantum Bose Brayton engine is established, in which finite-time processes and irreversibilities in two adiabatic processes are taken into account. Based on the model, expressions for the power output and the efficiency are derived. By using a numerical computation, the optimal relationship between the power output and the efficiency of an irreversible Bose Brayton engine is obtained. The optimal regions of the power output and the efficiency are determined. It is found that the influences of the irreversibility and the quantum degeneracy on the main performance parameters of the Bose Brayton engine are remarkable. The results obtained in the present paper can provide some new theoretical information for the optimal design and the performance improvement of a real Brayton engine.     

工质变比热条件下内燃机循环普适特性

用有限时间热力学的方法分析空气标准不可逆内燃机循环,导出了考虑工质变比热情况下,存在摩擦及传热损失时,由两个加热过程、两个放热过程和两个绝热过程组成的普适的空气标准不可逆内燃机循环的功率与压缩比、效率与压缩比以及功率和效率的最佳特性关系,同时由数值计算分析了工质变比热和循环过程对循环性能的影响特点,比较了工质恒、变比热时循环性能差异。所得结果包含了不可逆往复式Diesel、Otto、Brayton、Atkinson、Dual和Miller 循环的性能特性。     

Maximum power output of a class of irreversible non-regeneration heat engines with a non-uniform working fluid and linear phenomenological heat transfer law

Maximum power output of a class of irreversible non-regeneration heat engines with non-uniform working fluid, in which heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law [q ∝ Δ(T ⁻¹)], are studied in this paper. Optimal control theory is used to determine the upper bounds of power of the heat engine for the lumped-parameter model and the distributed-parameter model, respectively. The results show that the maximum power output of the heat engine in the distributed-parameter model is less than or equal to that in the lumped-parameter model, which could provide more realistic guidelines for real heat engines. Analytical solutions of the maximum power output are obtained for the irreversible heat engines working between constant temperature reservoirs. For the irreversible heat engine operating between variable temperature reservoirs, a numerical example for the lumped-parameter model is provided by numerical calculation. The effects of changes of reservoir’s temperature on the maximum power of the heat engine are analyzed. The obtained results are, in addition, compared with those obtained with Newtonian heat transfer law [q ∝ Δ(T)].     

A mixed cycle for converting heat to mechanical work

The subject of this study is to compare two different methods of converting heat to mechanical work. The first one is the well known Rankine cycle, which uses a pure substance as the working fluid. The second one is a power cycle which uses a mixture of substances with different boiling points as the working fluid. For convenience, this cycle will be called the mixed cycle hereafter.Since the conventional Rankine cycle has been analyzed by many other authors, we will focus on the mixed cycle. The main difference between the two is that, in the mixed cycle, steam is released by heating a mixture. The initial working fluid is created as the expanded steam is absorbed by a mixture of lower concentration at lower temperature and pressure.The main disadvantages of the mixed cycle are the upper temperature limit and the larger mass circulation.In order to illustrate the “efficiency limits” of the mixed cycle, a theoretical analysis is presented, in which all processes are considered to be ideal.     

Optimal configuration of a class of endoreversible heat engines for maximum efficiency with radiative heat transfer law

Optimal configuration of a class of endoreversible heat engines with fixed duration, input energy and radiative heat transfer law (q ∝ Δ(T ⁴)) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using optimal-control theory, and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches, four maximum-efficiency branches, and two adiabatic branches. The interval of each branch is obtained, as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton’s heat transfer law for the maximum efficiency objective, those with linear phenomenological heat transfer law for the maximum efficiency objective, and those with radiative heat transfer law for the maximum power output objective.     

Quantum Heat Engines with Complex Working Media,Complete Otto Cycles and Heuristics

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.     

Thermodynamic performance characteristics of a three-terminal quantum dot hybrid thermoelectric heat engine

We propose a new model of the three-terminal quantum dot hybrid thermoelectric heat engine in which the electrons transfer between two electronic terminals at different temperatures and chemical potentials through two coupled single-level quantum dots. Based on master equation we derive the expressions for the output power and the efficiency. The working region of the hybrid heat engine is determined according to the first and second law of thermodynamics. The performance characteristic curves are plotted and the optimal performance parameters are obtained. Finally, the influence of the non-radiative effect on the optimal performance parameters is discussed in detail.     

一类不可逆热机的热经济学优化性能

基于一类不可逆热机的一般循环模型,以每单位成本的功率输出作为热经济学目标函数,研究投资成本、燃料成本、其它费用成本和几种主要不可逆性对热机性能的影响。导出热机效率和热经济学目标函数间的基本优化关系。由此计算了最大热经济学目标函数及其对应的热机性能参数,给出了在不同传热规律下热机的基本优化关系。确定了热机的最佳工作区域和重要性能参数的界限。     

玻色气体的量子简并性对不可逆布雷顿制冷循环性能的影响

基于不可逆布雷顿制冷循环模型和理想玻色气体的状态方程,导出以玻色气体为工质的布雷顿制冷循环的输入功、制冷系数、制冷量等重要参数的表示式,由此讨论玻色气体的量子简并性和不可逆绝热过程对循环性能的影响,揭示以玻色气体为工质的不可逆布雷顿制冷循环的一般性能特性,从而导出一些重要结论．进而给出几种特殊情况下循环的性能特性．得到的结果有助于进一步了解经典布雷顿制冷循环和量子布雷顿制冷循环之间的区别和联系．