Four-Objective Optimizations for an Improved Irreversible Closed Modified Simple Brayton Cycle

An improved irreversible closed modified simple Brayton cycle model with one isothermal heating process is established in this paper by using finite time thermodynamics. The heat reservoirs are variable-temperature ones. The irreversible losses in the compressor, turbine, and heat exchangers are considered. Firstly, the cycle performance is optimized by taking four performance indicators, including the dimensionless power output, thermal efficiency, dimensionless power density, and dimensionless ecological function, as the optimization objectives. The impacts of the irreversible losses on the optimization results are analyzed. The results indicate that four objective functions increase as the compressor and turbine efficiencies increase. The influences of the latter efficiency on the cycle performances are more significant than those of the former efficiency. Then, the NSGA-II algorithm is applied for multi-objective optimization, and three different decision methods are used to select the optimal solution from the Pareto frontier. The results show that the dimensionless power density and dimensionless ecological function compromise dimensionless power output and thermal efficiency. The corresponding deviation index of the Shannon Entropy method is equal to the corresponding deviation index of the maximum ecological function.     

Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Diesel Cycle

Applying finite time thermodynamics theory and the non-dominated sorting genetic algorithm-II (NSGA-II), thermodynamic analysis and multi-objective optimization of an irreversible Diesel cycle are performed. Through numerical calculations, the impact of the cycle temperature ratio on the power density of the cycle is analyzed. The characteristic relationships among the cycle power density versus the compression ratio and thermal efficiency are obtained with three different loss issues. The thermal efficiency, the maximum specific volume (the size of the total volume of the cylinder), and the maximum pressure ratio are compared under the maximum power output and the maximum power density criteria. Using NSGA-II, single-, bi-, tri-, and quadru-objective optimizations are performed for an irreversible Diesel cycle by introducing dimensionless power output, thermal efficiency, dimensionless ecological function, and dimensionless power density as objectives, respectively. The optimal design plan is obtained by using three solution methods, that is, the linear programming technique for multidimensional analysis of preference (LINMAP), the technique for order preferences by similarity to ideal solution (TOPSIS), and Shannon entropy, to compare the results under different objective function combinations. The comparison results indicate that the deviation index of multi-objective optimization is small. When taking the dimensionless power output, dimensionless ecological function, and dimensionless power density as the objective function to perform tri-objective optimization, the LINMAP solution is used to obtain the minimum deviation index. The deviation index at this time is 0.1333, and the design scheme is closer to the ideal scheme.     

Four-Objective Optimization for an Irreversible Porous Medium Cycle with Linear Variation in Working Fluid’s Specific Heat

Considering that the specific heat of the working fluid varies linearly with its temperature, this paper applies finite time thermodynamic theory and NSGA-II to conduct thermodynamic analysis and multi-objective optimization for irreversible porous medium cycle. The effects of working fluid’s variable-specific heat characteristics, heat transfer, friction and internal irreversibility losses on cycle power density and ecological function characteristics are analyzed. The relationship between power density and ecological function versus compression ratio or thermal efficiency are obtained. When operating in the circumstances of maximum power density, the thermal efficiency of the porous medium cycle engine is higher and its size is less than when operating in the circumstances of maximum power output, and it is also more efficient when operating in the circumstances of maximum ecological function. The four objectives of dimensionless power density, dimensionless power output, thermal efficiency and dimensionless ecological function are optimized simultaneously, and the Pareto front with a set of solutions is obtained. The best results are obtained in two-objective optimization, targeting power output and thermal efficiency, which indicates that the optimal results of the multi-objective are better than that of one-objective.     

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.     

Optimal Heat Exchanger Area Distribution and Low-Temperature Heat Sink Temperature for Power Optimization of an Endoreversible Space Carnot Cycle

Using finite-time thermodynamics, a model of an endoreversible Carnot cycle for a space power plant is established in this paper. The expressions of the cycle power output and thermal efficiency are derived. Using numerical calculations and taking the cycle power output as the optimization objective, the surface area distributions of three heat exchangers are optimized, and the maximum power output is obtained when the total heat transfer area of the three heat exchangers of the whole plant is fixed. Furthermore, the double-maximum power output is obtained by optimizing the temperature of a low-temperature heat sink. Finally, the influences of fixed plant parameters on the maximum power output performance are analyzed. The results show that there is an optimal temperature of the low-temperature heat sink and a couple of optimal area distributions that allow one to obtain the double-maximum power output. The results obtained have some guidelines for the design and optimization of actual space power plants.     

热光伏能量转换器件的热力学极限与优化性能预测

受不可逆损失的影响,热光伏能量转换器件在高品位热能回收与利用方面受到限制.本文揭示不可逆损失来源,提供热光伏能量转换器件性能提升方案.利用半导体物理和普朗克热辐射理论,确定热光伏能量转换器件在理想条件下的最大效率.进而考虑Auger与Shockley-Reed-Hall非辐射复合和不可逆传热损失对光伏电池的电学、光学和热学特性的影响,预测热光伏器件优化性能.确定功率密度、效率和光子截止能量的优化区间.结果表明:相比于理想热光伏器件,非理想热光伏器件的开路电压、短路电流密度和效率有所降低;优化热光伏电池电压、光子截止能量和热源温度,可提升器件的功率密度和效率.通过对比发现理论与实验结果较一致,所得结果可为实际热光伏能量转换器件的研制提供理论指导.     

两级中冷回热再热布雷顿热电联产装置的性能

应用有限时间热力学理论和方法建立了恒温热源不可逆两级中冷回热再热布雷顿热电联产装置模型,基于分析的观点,导出了装置无量纲输出率和效率的解析式。在给定总压比的情形下,通过数值计算分别研究了输出率和效率与两个中冷压比和两个再热压比的关系,当总压比变化时,发现输出率和效率对总压比存在最大值,并分别求出了两个相应的最佳的中冷压比和再热压比。分析了回热度、中冷度、再热度、压气机和涡轮机效率、压降损失等特征参数对装置性能的影响。最后发现分别存在最佳的用户侧温度使输出率和效率取得双重最大值。     

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。     

Finite time thermodynamic analysis of quantum Otto heat engine with squeezed thermal bath

We investigate the finite time performance of reciprocating quantum Otto heat engine coupled to squeezed hot reservoir. We emphasize the converged limit cycle where each stroke is performed in finite time. To fully exploit the quantum availability provided by the squeezed bath, an optimal frequency protocol in the work extraction stroke is explicitly proposed. The power output is optimized with respect to the hot and cold isochore times. Thermodynamic analysis shows that for a wide range of squeezing parameters, efficiency at maximum power exceeds the generalized Curzon–Ahlborn efficiency defined by the effective temperature of the squeezed bath.     

Performance of a quantum heat engine cycle working with harmonic oscillator systems

A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are dis-cussed in brief.     

Efficiency at Maximum Power Output of a Quantum-Mechanical Brayton Cycle

The performance in finite time of a quantum-mechanical Brayton engine cycle is discussed, without intro- duction of temperature. The engine model consists of two quantum isoenergetic and two quantum isobaric processes, and works with a single particle in a harmonic trap. Directly employing the finite-time thermodynamics, the efficiency at maximum power output is determined. Extending the harmonic trap to a power-law trap, we find that the efficiency at max/mum power is independent of any parameter involved in the model, but depends on the confinement of the trapping potential.     

温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.     

Optimal performance at arbitrary power of minimally nonlinear irreversible thermoelectric generators with broken time-reversal symmetry

We investigate the performance at arbitrary power of minimally nonlinear irreversible thermoelectric generators (MNITGs) with broken time-reversal symmetry within linear irreversible thermodynamics, and the efficiency of MNITGs at arbitrary power is analytically derived. Furthermore, a universal bound on the efficiency of thermoelectric generators (TGs) with broken time-reversal symmetry and the arbitrary power is obtained. Some system-specific characteristics are discussed and uncovered. A large efficiency at arbitrary power can also be achieved via the cooperative mechanism between the system parameters. Our results indicate that the broken time-reversal symmetry provides the physically allowed degrees of freedom for tuning the performance of thermoelectric devices, and the physical trade-off region between the efficiency and the power output can also offer the appropriate space for optimizing the performance of TGs.     

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.     

Optimization Modeling of Irreversible Carnot Engine from the Perspective of Combining Finite Speed and Finite Time Analysis

An irreversible Carnot cycle engine operating as a closed system is modeled using the Direct Method and the First Law of Thermodynamics for processes with Finite Speed. Several models considering the effect on the engine performance of external and internal irreversibilities expressed as a function of the piston speed are presented. External irreversibilities are due to heat transfer at temperature gradient between the cycle and heat reservoirs, while internal ones are represented by pressure losses due to the finite speed of the piston and friction. Moreover, a method for optimizing the temperature of the cycle fluid with respect to the temperature of source and sink and the piston speed is provided. The optimization results predict distinct maximums for the thermal efficiency and power output, as well as different behavior of the entropy generation per cycle and per time. The results obtained in this optimization, which is based on piston speed, and the Curzon–Ahlborn optimization, which is based on time duration, are compared and are found to differ significantly. Correction have been proposed in order to include internal irreversibility in the externally irreversible Carnot cycle from Curzon–Ahlborn optimization, which would be equivalent to a unification attempt of the two optimization analyses.     

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。     

Exergetic efficiency optimization for an irreversible heat pump working on reversed Brayton cycle

This paper deals with the performance analysis and optimization for irreversible heat pumps working on reversed Brayton cycle with constant-temperature heat reservoirs by taking exergetic efficiency as the optimization objective combining exergy concept with finite-time thermodynamics (FTT). Exergetic efficiency is defined as the ratio of rate of exergy output to rate of exergy input of the system. The irreversibilities considered in the system include heat resistance losses in the hot- and cold-side heat exchangers and non-isentropic losses in the compression and expansion processes. The analytical formulas of the heating load, coefficient of performance (COP) and exergetic efficiency for the heat pumps are derived. The results are compared with those obtained for the traditional heating load and coefficient of performance objectives. The influences of the pressure ratio of the compressor, the allocation of heat exchanger inventory, the temperature ratio of two reservoirs, the effectiveness of the hot- and cold-side heat exchangers and regenerator, the efficiencies of the compressor and expander, the ratio of hot-side heat reservoir temperature to ambient temperature, the total heat exchanger inventory, and the heat capacity rate of the working fluid on the exergetic efficiency of the heat pumps are analysed by numerical calculations. The results show that the exergetic efficiency optimization is an important and effective criterion for the evaluation of an irreversible heat pump working on reversed Brayton cycle.     

Ecological optimization of an irreversible harmonic oscillators Carnot heat engine

A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.     

Thermodynamic Performance Analysis of a Waste Heat Power Generation System (WHPGS) Applied to the Sidewalls of Aluminum Reduction Cells

To recover energy from the waste heat of aluminum reduction cells, a waste heat power generation system (WHPGS) with low boiling point working fluid based on Organic Rankine Cycle was proposed. A simplified model for the heat transfer around the walls of aluminum reduction cells and thermodynamic cycle was established. By using the model developed and coded in Matlab, thermal performance analysis of the system was conducted. Results show that the electrolyte temperature and the freeze ledge thickness in the cell can significantly affect the heat absorption of the working fluid in the heat exchange system on the walls. Besides, both the output power and the thermal efficiency of the power generation system increase with the system pressure. The output power and thermal efficiency of the system can also be affected by the type of working fluid used in the system. Working fluids for the best system performance under different output pressures were determined, based on the performance analysis. This WHPGS would be a good solution of energy-saving in aluminum electrolysis enterprises.     

Recent advance on the efficiency at maximum power of heat engines

This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman's ratchet as a heat engine are presented. It is found that: the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.