Effects of unequal finite piston speeds on the optimal performances of endoreversible Carnot refrigeration and heat pump cycles

The performances of endoreversible Carnot refrigeration and heat pump cycles with loss of heat resistance and finite piston speeds are analysed and optimized by using the combination of finite time thermodynamics, finite speed thermodynamics and direct method. The unequal finite piston speed model on four branches is adopted. Expressions of cooling load of endoreversible Carnot refrigeration cycle and of heating load of endoreversible Carnot heat pump cycle are derived with a fixed cycle period and unequal finite piston speeds on the four branches. Numerical examples show that there exist optimal expansion ratios, which lead to maximum cooling load and maximum heating load for the fixed coefficient of performance (COP), respectively. The maximum cooling load, maximum heating load, optimal ratios of finite piston speeds and optimal hot- and cold-side working fluid temperatures versus COP characteristics for the endoreversible Carnot refrigeration and heat pump cycles are obtained. Moreover, the effects of design parameters on the performances of the two cycles are discussed.     

A universal expression for optimum specific work of reciprocating heat engines having endoreversible carnot efficiencies

Irreversible heat transfer (finite time) analysis is used to obtain the optimum thermodynamic specific work potential at maximum power for various practical reciprocating cycles having endoreversible Carnot efficiencies. The theory of finite‐time thermodynamics for reciprocating endoreversible cycles with heat transfer irreversibilities gives rise to an optimum efficiency at maximum power output, of η=1−(T_L/T_H)^0·5 for Carnot‐like cycles in contrast to the upper limit for Carnot‐like cycles of η=1−(T_L/T_H) obtained from infinite‐time thermodynamics. It is shown here that, additionally, for this same general family of regenerative reciprocating cycles which includes the Stirling, the Ericsson and the reciprocating Carnot cycle, the finite‐time optimum specific work output at maximum power, (w_opt), is exactly half of that obtained for infinite‐time reversible cycles (Carnot work, w_rev) operating between the same temperature limits (i.e., w_opt=½w_rev). To accomplish this, the analysis makes use of time symmetry to minimize overall cycle time and to thus optimize net cycle power. Based on linear heat transfer laws, the expression for optimum specific work is shown to be independent of heat conductances. Moreover, this optimum specific work output is the same expression for all of the members of this family of cycles. This analysis makes use of the ideal gas model with constant specific heats, though the results are shown to be universal for the Carnot cycle for vapours and real gases. A sample calculation is given which shows that while operating under the same optimized conditions, the endoreversible Stirling engine will have the same thermal efficiency as the endoreversible Ericsson, but will have a higher optimum power output. The optimum power of the reciprocating endoreversible Carnot engine will be superior to both. Copyright © 1999 John Wiley & Sons, Ltd.     

广义不可逆卡诺热机的生态学最优性能

以反映热机功率与熵产率之间最佳折衷的“生态学”准则为目标，综合考虑热阻、热漏及其它不可逆性对卡诺热机性能的影响，导出牛顿传热规律下循环的生态学最优性能，由数值计算分析比较了热漏、内不可逆性的影响特点。生态学优化以牺牲小部分输出功率为代价，较大地降低了循环的熵产率，而且在一定程度上提高了热机效率。因此，生态学目标函数不仅反映了输出功率和熵产率之间的最佳折衷，而且反映了输出功率和热效率之间的最佳折衷。     

有限速率过程对活塞式斯特林发动机性能的影响

本文讨论在给定热源温度和压缩比的情况下,过程进行的速率有限,并受热传导不可逆影响的内可逆活塞式斯特林发动机的最优性能,导出以理想气体或范德瓦尔斯气体为工质的斯特林发动机的最大输出功率与热效率的关系,以及最大热效率与输出功率的关系,并推出了一些新的有限时间热力学的性能界限。     

包含6种热机模型的普适内可逆热机循环(火用)经济性能优化

用有限时间热力学方法分析了工作在恒温热源TH、TL之间的普适定常流内可逆热机循环模型的炯经济性能,导出了循环利润率与工质温比、热效率与工质温比的关系式,以及利润率和效率的特性关系,并由数值计算分析了循环过程对循环性能的影响特点。所得结果包含了内可逆Carnot、Diesel、Otto、Atkinson、Brayton和Dual循环的有限时间炯经济性能。     

有限时间内不可逆卡诺热机的不可逆因子的研究

推导出了有限时间内不可逆卡诺热机的不可逆因子计算式,同时指出,其最大功率时不可逆因子无法仅用高、低温热源的温度来确定,还必须已知系统循环工质的某一端的温度。由实例计算证明了不可逆因子计算式的可信性,此计算公式对有限时间内不可逆卡诺热机的不可逆损失及热效率的计算有一定的指导意义。     

一类不可逆卡诺热机最佳效率和功率间的关系

采用包括Ｄｕｌｏｎｇ－Ｐｅｔｉｔ非线性传热率和热漏的不可逆卡诺热机模型,导出其基本优化关系,并讨论了热机在最大输出功率时的效率问题。     

线性唯象传热定律下广义不可逆卡诺热机的频率特性

以广义不可逆卡诺热机模型为研究对象,考虑工质与热源间传热服从线性唯象定律,研究热机性能与循环频率的关系.得到了不同于内可逆情况下的输出功率、效率以及可利用温差与循环频率和吸、放热时间比的关系式,通过数值计算,分析了热漏、内不可逆性的影响特点.结果表明,在任一循环吸、放热时间比下,存在一个最佳循环频率,使循环输出功率达到最大;存在热漏时,任一循环吸、放热时间比下,存在一个最佳循环频率,使循环效率达到最大.     

Optimal regenerator performance in Stirling engines

The key component of a Stirling engine is its regenerative heat exchanger. This device is subject to losses due to dissipation arising from the flow through the regenerator as well as due to imperfect heat transfer between the regenerator material and the gas. The magnitudes of these losses are characterized by the Stanton number St and the Fanning friction factor f, respectively. Using available data for the ratio St/f, results are found for the Carnot efficiency and the power output of the regenerator. They depend on the conductance and on the ratio of pressures at the two sides of the regenerator. Optimum results for efficiency and power output of the regenerator are derived in the limit of zero Mach number. The results are applied to the Stirling engine. The efficiency and the power output of the engine are found for given amplitude of the compression piston. Optimization with respect to regenerator conductance and piston phase angle leads to a maximum possible value of the power output. Under optimal conditions, the Carnot efficiency just below this maximum is close to 100%. Copyright © 2009 John Wiley & Sons, Ltd.     

Power optimization of a finite-time Carnot heat engine

The power output of a simple, finite-time Carnot heat engine is studied. The model adopted is a reversible Carnot cycle coupled to a heat source and a heat sink by heat transfer. Both the heat source and the heat sink have finite heat-capacity rates. A mathematical expression is derived for the power output of the irreversible heat engine. The maximum power output is found. The maximum bound provides the basis for designing a real heat engine and for a performance comparison with existing power plants.     

Optimal performance of a spin quantum Carnot heat engine with multi-irreversibilities

By using quantum master equation, semi-group approach and finite time thermodynamics (FTT), this paper derives the expressions of cycle period, power and efficiency of an irreversible quantum Carnot heat engine with irreversibilities of heat resistance, internal friction and bypass heat leakage, and provides detailed numerical examples. The irreversible quantum Carnot heat engine uses working medium consisting of many non-interacting spin-1/2 systems and its cycle is composed of two isothermal processes and two irreversible adiabatic processes. The optimal performance of the quantum heat engine at high temperature limit is deduced and analyzed by numerical examples. Effects of internal friction and bypass heat leakage on the optimal performance are discussed. The endoreversible case, frictionless case and the case without bypass heat leakage are also briefly discussed.     

热漏对热机功率效率特性的影响分析

在以往文献的基础上,对定常态流不可逆卡诺热机的热漏模型进行了改进,将热机热漏分为外热漏和内热漏两种方式,分析两种热漏方式对不可逆热机最优性能的影响。分析得出内热漏对热机功率效率特性的影响不同于外热漏,也与摩擦,涡流和非平衡等各种不可逆效应不同,内热漏应单独作为影响热机特性的一种因素。并导出存在热阻和两种热漏损失的热机存在最佳功率和最佳效率两种工作状态,两种工作状态分别对应不同的面积比。所得结果对热机设计具有一定指导意义。     

复杂热源下不可逆诺维科夫热机最大功率输出

考虑实际热机工作下的旁通热漏和内部耗散等不可逆因素,建立了包括连续均匀分布、三角形分布、二次分布和帕累托分布等四种不同的统计概率分布高温热源温度下的广义不可逆诺维科夫热机模型,导出了热机最大输出功率及相应的热效率和熵产率随高温热源温度、内部不可逆性等因素变化的关系式。结果表明：热漏和内部耗散分别对热机性能有着不同的影响,热漏使统计热源温度分布下最大功率输出对应的热效率减小,同时也增大了熵产率,但对热机的最大功率输出无影响;内部耗散不可逆性使热机的最大输出功率及相应热效率均明显减小,但使熵产率先增大后减小;熵产率随高温热源温度的标准差增大而减小。研究结果对太阳能发电厂性能提升具有一定理论指导意义。     

不同优化准则下斯特林发动机的性能分析

应用有限时间热力学原理.建立了一个考虑热阻、热漏和回热损失等不可逆因素的斯特林发动机模型;推导了最大输出功率、最大效率和生态学优化准则下,斯特林发动机性能的表达式;比较了三种优化准则下,热漏系数和回热器有效性对斯特林发动机性能的影响.研究表明:对热漏损失和回热损失较大的斯特林发动机,宜选用生态学优化准则.为斯特林发动机...     

卡诺热机的最佳利润与效率间的关系

本文导出牛顿定律系统卡诺热机的最佳利润与效率间的关系,并得到最大利润时的效率界限。其结果包含了最大功率和最小熵产率(也即最小损失)两种特例。籍此,作者首次提出了有限时间经济分析和有限时间经济性能界限的概念,为统一现代热力学的各分支研究开拓了方向。     

补燃型不可逆联合循环热机的性能分析

在原有的不可逆联合动力循环模型的基础上,建立了一个存在热阻、热漏、补燃、内不可逆性的定常流联合卡诺热机循环模型。研究其在补燃作用下的功率和效率特性并对其进行优化,导出功率、效率的基本优化关系,分析了补燃对最优性能的影响。     

Power-optimization of non-ideal energy converters under generalized convective heat transfer law via Hamilton-Jacobi-Bellman theory

A multistage irreversible 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∝m(ΔT)] and the irreversibility of heat resistance and internal dissipation is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations, which determine optimal fluid temperature configurations for maximum power output under the conditions of fixed duration and fixed initial temperature of the driving fluid. Based on general optimization results, the analytical solution for the case with Newtonian heat transfer law (m=1) is further obtained. Since there are no analytical solutions for the other heat transfer laws (m≠1), the continuous HJB equations are discretized and dynamic programming (DP) algorithm is adopted to obtain complete numerical solutions of the optimization problem, and the relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail.     

热漏对热机功率效率特性的影响

本研究热漏对热机最优性能的影响,导出存在热阻和热漏损失的定常态流不可逆热机的最佳功率、效率关系,所得结果不同于仅存在热阻损失的内可逆热机的功率效率特性关系,且与实际热机特性较为一致,由此指出了一些献的“不可逆循环”模型的不完备之处。     

有限时间热力学中不可逆卡诺热机

对几种不可逆卡诺热机模型作了述评,并提出一种新的不可逆卡诺热机模型。此外,还强调了有限时间热力学中研究不可逆热机时,必须考虑不可逆性对功率的影响。     

Development of Hybrid Solar Systems Using Solar Thermal,Photovoltaics, and Wind Energy Translation from “Journal of the Japanese Solar Energy Society,” Volume 11, Number 4, page 15

Finite time exergoeconomic performance optimization of a universal irreversible heat-engine cycle model, which consists of two constant thermal-capacity heating branches, two constant thermal-capacity cooling branches and two adiabatic branches, is investigated by taking the profit rate criterion as the optimization objective. The analytical formulae for power, efficiency and profit rate function of the universal irreversible heat-engine cycle model with the losses of heat transfer, heat leakage and internal irreversibility are derived. The focus of this article is to search the compromised optimization between economics (profit rate) and the energy utilization factor (efficiency) for irreversible cycles. Moreover, analysis and optimization of the model are carried out in order to investigate the effects of these losses and cycle process on the performance of the universal irreversible heat-engine cycle model using numerical examples. The results obtained herein include the performance characteristics of seven typical irreversible heat engines, including Carnot, Diesel, Otto, Atkinson, Brayton, Dual and Miller cycles.