回热式变温热源空气制冷循环容积制冷率优化

考虑热阻损失、压缩机与膨胀机的内损失及管路系统的压力损失，研究一个比较接近实际装置的回热式交温热源空气制冷循环，得出了循环容积制冷率制冷系数的解析关系式。由数值计算分析了压比、热导率分配以及工质与热源间的热容率匹配等参数对容积制冷率的影响。     

Performance analysis of a closed regenerated Brayton heat pump with internal irreversibilities

This paper analyses the performance of a real heat pump plant via methods of entropy generation minimization or finite‐time thermodynamics. The analytical relations between heating load and pressure ratio, and between coefficient of performance (COP) and pressure ratio of real closed regenerated Brayton heat pump cycles coupled to constant‐ and variable‐temperature heat reservoirs are derived. In the analysis, the irreversibilities include heat transfer‐irreversible losses in the hot‐ and cold‐side heat exchangers and the regenerator, the non‐isentropic expansion and compression losses in the compressor and expander, and the pressure drop loss in the pipe and system. The optimal performance characteristics of the cycle may be obtained by optimizing the distribution of heat conductances or heat transfer surface areas among the two heat exchangers and the regenerator, and the matching between working fluid and the heat reservoirs. The influence of the effectiveness of regenerator, the effectiveness of hot‐ and cold‐side heat exchangers, the efficiencies of the expander and compressor, the pressure recovery coefficient and the temperature of the heat reservoirs on the heating load and COP of the cycle are illustrated by numerical examples. Published in 1999 by John Wiley & Sons, Ltd.     

Optimum allocation of heat exchanger inventory of irreversible air heat pump cycles

This study has determined the optimal ratios of heat conductance of a cold-side heat exchanger to that of a hot-side heat exchanger when the heating load and the coefficient of performance (COP) of the irreversible air heat pump cycles are taken as the optimization objectives. Both the optimum distributions of heat conductance corresponding to the maximum heating load and the maximum COP are less than 0.5 for the fixed total heat exchanger inventory. The influences of the heat reservoir temperature ratio, the total heat exchanger inventory, and the efficiencies of the compressor and expander on the optimum distribution of heat conductance and the maximum heating load and the maximum COP are analysed and shown by numerical examples.     

Power optimization of an endoreversible closed intercooled regenerated Brayton cycle

In this paper, power is optimized for an endoreversible closed intercooled regenerated Brayton cycle coupled to constant-temperature heat reservoirs in the viewpoint of finite-time thermodynamics (FTT) or entropy generation minimization (EGM). The effects of some design parameters, including the cycle heat reservoir temperature ratio and total heat exchanger inventory, on the maximum power and the corresponding efficiency are analyzed by numerical examples. The analysis shows that the cycle dimensionless power can be optimized by searching the optimum heat conductance distributions among the hot- and cold-side heat exchangers, the regenerator and the intercooler for fixed total heat exchanger inventory, and by searching the optimum intercooling pressure ratio. When the optimization is performed with respect to the total pressure ratio of the cycle, the maximum dimensionless power can be maximized again.     

不可逆半导体固态热离子制冷器性能分析和优化

建立了考虑外部有限速率传热过程和热源间热漏的不可逆半导体固态热离子制冷器模型,基于非平衡热力学和有限时间热力学理论导出了热离子制冷器的制冷率和制冷系数的表达式;对比分析了不可逆热离子制冷器与可逆热离子制冷器的发射电流密度特性、电极温度特性以及制冷系数特性;研究了不可逆系统的制冷率与制冷系数最优性能,得到了制冷率和制冷系数的最优运行区间;通过数值计算,详细讨论了外部传热以及内部导热、热源间热漏损失、热源温度、外加电压、半导体材料势垒等设计参数对热离子装置性能的影响。在总传热面积一定的条件下,进一步优化了高、低温侧换热器的面积分配以获得最佳的制冷率和制冷系数特性。结果表明,由于存在内部和外部的不可逆性,热离子装置的发射电流密度及制冷系数都会明显降低;不可逆半导体固态热离子制冷器的制冷率与制冷系数特性呈扭叶型;合理地选外加电压、势垒等参数,可以使制冷器设计于最大制冷率或最大制冷系数的状态。     

Ecological optimization of an irreversible Ericsson cryogenic refrigerator cycle

The ecological optimization and parametric study of an irreversible Ericsson cryogenic refrigerator cycle with finite heat capacities of external reservoirs is studied. The ecological function is defined as the cooling load minus the loss of the cooling load (the irreversibility) due to the entropy generation rate. The ecological function is optimized with respect to working fluid temperatures and the values of the cooling load, power input, the loss rate of the cooling load and COP are calculated for a typical set of operating parameters. The effects of different operating parameters on the ecological function, cooling load, the loss rate of the cooling load and COP are studied. The loss rate of the cooling load and the power input are found to be increasing functions of the cycle temperature ratio and decreasing functions of COP while the COP is found to be a decreasing function of the cycle temperature ratio. On the other hand, there exist the optimal values of the cycle temperature ratio and COP at which the ecological function and cooling load attain their maximum values. Also the ecological function and the cooling load are found to be increasing functions of the sink‐side heat capacitance rate and the effectiveness on the source‐, sink‐, and regenerative‐side heat exchangers while the decreasing functions of the source‐side heat capacitance rate. Copyright © 2005 John Wiley & Sons, Ltd.     

Finite time thermodynamic analysis of an irreversible regenerative closed cycle brayton heat engine

This communication presents the parametric study of an irreversible regenerative Brayton cycle with nonisentropic compression and expansion processes for finite heat capacitance rates of external reservoirs. The power output of the cycle is maximized with respect to the working fluid temperatures and the expressions for maximum power output and the corresponding thermal efficiency are obtained. The effect of the effectiveness of the various heat exchangers and the efficiencies of the turbine and compressor, the reservoir temperature ratio and the heat capacitance rate of heating and cooling fluids and the cycle working fluid on the power output and the corresponding thermal efficiency has been studied. It is seen the effect of cold side effectiveness is more pronounced for the power output while the effect of regenerative effectiveness is more pronounced for the thermal efficiency. It is found that the effect of turbine efficiency is more than the compressor efficiency on the performance of these cycles. It is also found that the effect of sink-side heat capacitance rate is more pronounced than the heat capacitance rate on the source side and the heat capacitance rate of the working fluid.     

变温热源内可逆中冷回热布雷顿循环功率密度优化

以功率密度为目标,用有限时间热力学的方法,通过数值计算,对变温热源条件下的内可逆中冷回热布雷顿循环的高、低温侧换热器的热导率分配和中间压比、循环总压比和工质与热源间的热容率匹配进行优化。分别得到了最大功率密度、双重最大功率密度和三重最大功率密度,并分析了热力学参数对高低温侧换热器的热导率最优分配、最佳中间压比、最大功率密度和双重最大功率密度的影响。     

Cooling load and coefficient of performance optimizations for real air-refrigerators

Based on a simple irreversible variable-temperature heat reservoir air (Brayton) refrigeration cycle model, a performance analysis and optimization of a real air refrigerator is carried out using finite-time thermodynamics. To maximize the cooling load and the coefficient of performance (COP) of the cycle, the allocation of a fixed total heat-exchanger inventory and thermal-capacity rate matching between the working fluid and heat reservoirs are optimized, respectively. The influences of pressure ratio, the total heat-exchanger inventory, the efficiencies of the compressor and expander, the thermal capacity rate of the working fluid and the ratio of the thermal-capacity rates of the heat reservoirs on the performance of the cycle are shown by numerical examples. The results obtained provide guidances for the design of practical air-refrigeration plants.     

变温热源条件下内可逆闭式中冷回热布雷顿循环的功率优化

计入工质与高低浊侧换热器、回热器和中冷器的热阻损失以功率为优化目标，借助数值计算，研究了变温热源条件下内可逆闭式中冷回热布雷顿循环输出功率最大时，高低温侧换热器、回热器和中冷器的热导率分配以及中间压比与总压比的关系；分析了工质与热源间的热容率匹配对双重最大功率的影响。     

内可逆空气制冷机性能的生态学优化

基于[火用]分析的观点，运用有限时间热力学方法对内可逆空气制冷机进行生态学优化，导出了换热器热导最优分配时的最佳制冷功率、熵产率以及生态学（E）目标函数的解析式，进一步求得最大E目标值时的工质等熵温比（压比）界限及相应的制冷系数、制冷功率和熵产率；采用数值计算分析了热源温比、换热器总热导以及高温热源温度和环境温度之比对该制冷机生态学最优性能的影响。结果表明：生态学目标函数不仅反映了[火用]输出率和熵产率之间的最佳折衷，而且也反映了制冷功率和制冷系数之间的最佳折衷。     

An analysis of the heat transfer rate and efficiency of TE (thermoelectric) cooling systems

The heat transfer rate and efficiency of TE (thermoelectric) cooling systems were investigated. The emphasis of the present study is focused on the use of large-scale TE refrigerators for air conditioning applications. A one-dimensional heat transfer analysis was performed to determine the cooling power and electricity consumption of the TE elements. The constant-property results are in good agreement with the variable-property solutions for TE materials and temperatures typical for air conditioning applications. A heat transfer analysis was also carried out for TE refrigerators equipped with a heat exchanger. Both parallel- and counter-flow heat exchangers were considered. Fluid temperature variations of these two flow arrangements were found to be quite different, but the efficiencies and cold fluid exit temperatures differed only slightly when a uniform current was used for all TE elements. If the length of the heat exchanger exceeds an optimal value, the cold fluid temperature begins to rise and the efficiency drops for both parallel- and counter-flow arrangements. The second law of thermodynamics was applied to the optimization of TE refrigerators operating between two constant-temperature reservoirs and between two flowing fluids. It was found that if a TE cooling system incorporates a heat exchanger, a nonuniform current distribution should be used to achieve the maximum efficiency and the lowest cold fluid temperature. The optimization results for TE refrigerators operating between two constant-temperature reservoirs are not applicable to TE cooling systems between two flowing fluids. The most energy-efficient current distribution for the parallel-flow arrangement is the one which increase in the direction of the cold fluid.     

Power,power density and efficiency optimization of an endoreversible Braysson cycle

The performance optimization of an endoreversible Braysson cycle with heat resistance losses in the hot- and cold-side heat exchangers is performed by using finite-time thermodynamics. The relations between the power output and the working fluid temperature ratio, between the power density and the working fluid temperature ratio, as well as between the efficiency and the working fluid temperature ratio of the cycle coupled to constant-temperature heat reservoirs are derived. Moreover, the optimum heat conductance distributions corresponding to the optimum dimensionless power output, the optimum dimensionless power density and the optimum thermal efficiency of the cycle, and the optimum working fluid temperature ratios corresponding to the optimum dimensionless power output and the optimum dimensionless power density are provided. The effects of various design parameters on those optimum values are studied by detailed numerical examples.     

Heating load,heating-load density and COP optimizations of an endoreversible air heat-pump

The finite-time thermodynamic performance has been studied of an endoreversible air heat-pump with constant-temperature heat-reservoirs. The heating load, the coefficient of performance (COP), and the heating-load density, i.e. the ratio of heating load to the maximum specific volume in the cycle, are the optimization objectives. The analytical formulae relating the heating load and pressure-ratio, between the COP and pressure-ratio, as well as between the heating-load density and pressure-ratio are derived assuming heat resistance losses occur in the hot- and cold-side heat-exchangers. The influences of the effectiveness of the heat-exchangers and the heat-reservoir temperature-ratio on the heating load, the COP and the heating-load density are analyzed. The cycle performance optimizations are performed by searching the optimal distribution of heat conductance of the hot- and cold-side heat-exchangers for the fixed total heat-exchanger inventory. The influences of some design parameters, including heat-capacity rate of the working fluid, heat-reservoir temperature-ratio and heat-exchanger inventory on the optimal distribution of heat conductance, the maximum heating load and the maximum heating-load density are indicated by numerical examples. The different results obtained from the heating-load optimization and the heating-load density optimization are shown. The air heat-pump design, with heat-loading density optimization, leads to smaller size equipment.     

Optimum allocation of heat transfer surface area for cooling load and COP optimization of a thermoelectric refrigerator

The theory of finite time thermodynamics is applied to analyze and optimize the performance of a thermoelectric refrigerator, which is composed of multi-elements. For the fixed total heat transfer surface area of two heat exchangers, the ratio of the heat transfer surface area of the high temperature side heat exchanger to the total heat transfer surface area of the heat exchangers is optimized for maximizing the cooling load and the coefficient of performance of the thermoelectric refrigerator. The effects of various parameters on the optimum performance are analyzed. The results may provide guides for the analysis and optimization of practical thermoelectric refrigerators.     

Power optimization of an endoreversible closed intercooled regenerated Brayton-cycle coupled to variable-temperature heat-reservoirs

In this paper, in the viewpoint of finite-time thermodynamics and entropy-generation minimization are employed. The analytical formulae relating the power and pressure-ratio are derived assuming heat-resistance losses in the four heat-exchangers (hot- and cold-side heat exchangers, the intercooler and the regenerator), and the effect of the finite thermal-capacity rate of the heat reservoirs. The power optimization is performed by searching the optimum heat-conductance distributions among the four heat-exchangers for a fixed total heat-exchanger inventory, and by searching for the optimum intercooling pressure-ratio. When the optimization is performed with respect to the total pressure-ratio of the cycle, the maximum power is maximized twice and a ‘double-maximum’ power is obtained. When the optimization is performed with respect to the thermal capacitance rate ratio between the working fluid and the heat reservoir, the double-maximum power is maximized again and a thrice-maximum power is obtained. The effects of the heat reservoir’s inlet-temperature ratio and the total heat-exchanger inventory on the optimal performance of the cycle are analyzed by numerical examples.     

恒温热源条件下不可逆闭式中冷回热布雷顿循环的功率优化

考虑高低温侧换热器、回热器和中冷器的热阻损失，以及压气机和涡轮中的不可逆损失，以功率为优化目标，借助数值计算，研究了恒温热源条件下不可逆闭式中冷回热布雷顿循环输出功率最大时高低温侧换热器、回热器和中冷器的热导率分配以及中间压力与总压比的关系。     

Effectiveness–NTU Relations for Counterflow Heat Exchangers: The Effect of Kinetic Energy Variation and Heat Leak From Outside

The effectiveness–number of transfer units (NTU) relations are useful data for designing and performance evaluation of heat exchangers with fluids having considerable variation in velocities in the presence of heat leak. In this article, the closed-form (benchmark) solutions for counterflow heat exchangers, when the heat leak is either on the hot or cold side of the heat exchanger in the presence of kinetic energy variation, are presented. It was found that the effectiveness depends on NTU and fluid capacity ratio along with six other dimensionless variables that reflect the magnitude and axial distribution of the kinetic energy and heat leak on the hot and cold sides of the heat exchanger. The results are also presented in a graphical form exhibiting the variation of effectiveness of the heat exchanger with the already-mentioned parameters. It was demonstrated that when the dimensionless heat leak and kinetic energy terms approach zero, the solution reduces to the classical effectiveness–NTU relations for counterflow heat exchangers.     

Second Law Efficiency Analysis of Heat Exchangers

Analytical analysis of unbalanced heat exchangers is carried out to study the second law thermodynamic performance parameter through second law efficiency by varying length‐to‐diameter ratio for counter flow and parallel flow configurations. In a single closed form expression, three important irreversibilities occurring in the heat exchangers—namely, due to heat transfer, pressure drop, and imbalance between the mass flow streams—are considered, which is not possible in first law thermodynamic analysis. The study is carried out by giving special influence to geometric characteristics like tube length‐to‐diameter dimensions; working conditions like changing heat capacity ratio, changing the value of maximum heat capacity rate on the hot stream and cold stream separately and fluid flow type, i.e., laminar and turbulent flows for a fully developed condition. Further, second law efficiency analysis is carried out for condenser and evaporator heat exchangers by varying the effectiveness and number of heat transfer units for different values of inlet temperature to reference the temperature ratio by considering heat transfer irreversibility. Optimum heat exchanger geometrical dimensions, namely length‐to‐diameter ratio can be obtained from the second law analysis corresponding to lower total entropy generation and higher second law efficiency. Second law analysis incorporates all the heat exchanger irreversibilities. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21109     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.