Stirling Refrigerating Machine Modeling Using Schmidt and Finite Physical Dimensions Thermodynamic Models: A Comparison with Experiments

The purpose of the study is to show that two simple models that take into account only the irreversibility due to temperature difference in the heat exchangers and imperfect regeneration are able to indicate refrigerating machine behavior. In the present paper, the finite physical dimensions thermodynamics (FPDT) method and 0-D modeling using the Schmidt model with imperfect regeneration were applied in the study of a β type Stirling refrigeration machine.The 0-D modeling is improved by including the irreversibility caused by imperfect regeneration and the finite temperature difference between the gas and the heat exchangers wall. A flowchart of the Stirling refrigerator exergy balance is presented to show the internal and external irreversibilities. It is found that the irreversibility at the regenerator level is more important than that at the heat exchangers level. The energies exchanged by the working gas are expressed according to the practical parameters, necessary for the engineer during the entire project. The results of the two thermodynamic models are presented in comparison with the experimental results, which leads to validation of the proposed FPDT model for the functional and constructive parameters of the studied refrigerating machine.     

以广义Redlich-Kwong气体为工质的不可逆回热式斯特林热机循环输出功率和效率

研究了热阻、回热损失和热漏等多种不可逆因素对以广义Redlich-Kwong气体为工质的斯特林热机性能的影响,给出了斯特林热机输出功率和效率的具体表达式并分析非理想回热特性及循环主要性能参数(如循环体积比及工质高低温比等)对循环输出功率和效率的影响.同时指出,只有在理想回热及无热漏的情况下,气体斯特林热机的效率才能达到卡诺效率.     

On the maximum efficiency of the ideal regenerative stirling cycle

It is shown that the efficiency of a regenerative Stirling cycle can principally not reach that of a Carnot cycle operating in the same temperature range. A relation is obtained between the degree of regeneration and the characteristics of regenerator. The maximum efficiency of an ideal regenerative Stirling engine is obtained.     

Optimisation thermodynamique en temps fini du moteur de Stirling endo- et exo-irréversible

Finite-time thermodynamics optimisation of an endo- exo-irreversible Stirling Motor. This work deals with the finite time thermodynamic optimization of a Stirling engine. An endo- and exo-irreversible cycle is considered. The internal irreversibilities are due to the internal conductance of the plant and to the non-adiabatic regenerator. Also, the general irreversibilities of the non-quasistatic cycle are taken into account. The external irreversibilities are due to the linear interactions between the heat sources and the working fluids at finite temperature gaps.A sensitivity analysis was performed in order to optimize the operation conditions leading to maximum power output. The results obtained are in good agreement with the experimental data.     

斯特林热机的基本优化关系及功率和效率界限

1前言近年来,有些学者应用有限时间热力学研究斯特林热机的优化性能,获得一些比经典热力学界限更有意义的新性能界限。但至今为数还较少,应继续开展研究。特别是有人提出“21世纪是斯特林热机的世纪’巾一］。本文将进一步研究受热阻、热漏和回热损失三种主要不可逆因素影响的斯特林热机的优化性能,导出热机的基本优化关系及功率和效率界限。结果表明,热漏的存在使斯特林热机的优化性能与无热漏时的有质的差异,而在热阻和回热损失的基础上再考虑热漏的影响,其结果将可反映出实际热机观测性能的主要特征【’,‘］,从而对实际更有指…     

不可逆太阳能Stirling热机性能优化及参数分析

建立不可逆太阳能Stirling热机循环系统,研究太阳能集热器辐射对流热损、有限速率热传导,回热器的回热损失及其它不可逆因素对系统性能的影响.基于热力学分析方法和最优控制理论,导出系统总效率和集热器工作温度所满足的优化方程,确定和评估相关性能界限和优化设计参数值,并详细讨论包括与传热系数有关的综合因子、回热损失因子以及...     

热声热机和斯特林热机振荡现象的网络描述

热力学循环的实质是一种非等熵的循环 ,热声热机和斯特林热机振荡现象在满足热力学循环一般规律的同时 ,而各有其特殊性 ,故其各自的振荡本质是有差异的 ,用于描述两者的网络模型也必然有差异。     

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.     

带有Dzyaloshinski-Mariya相互作用的两比特纠缠量子Otto热机和量子Stirling热机

研究了以带有Dzyaloshinski-Mariya(DM)相互作用的两比特自旋体系为工质的量子纠缠Otto热机和量子Stirling热机.两种不同热机在各自的循环过程中,通过保持其他参量不变,只有DM相互作用发生改变,从而分析热机循环中DM相互作用与热传递、做功以及效率等热力学量之间的关系.研究结果表明:DM相互作用对两种热机的基本量子热力学量都具有重要的影响,但量子Stirling热机由于回热器的使用,其循环效率会大于量子Otto纠缠热机的效率,甚至会超过Carnot效率;得到了量子Otto纠缠热机和量子Stirling热机做正功的条件.因此,在这两个纠缠体系中,热力学第二定律都依然成立.     

谐振电机耦合型双效斯特林燃气热泵系统研究

针对当前国家大力推行清洁能源技术和煤改气政策的供暖现状,本文探索了一种双效斯特林燃气热泵系统.全文基于热声学观点对系统进行了理论研究,并采用SAGE程序对其进行数值模拟和优化设计.计算表明,当加热、供热和冷端温度分别为923 K、333 K和273 K时,系统可获得的泵热量为7000 W,COPh为 1.79,系统?效...     

交变流动回热器的热声功能和回热功能

本文从解析的角度论证了交变流动回热器不仅具有经典热力学理论所认为的回热功能,而且具有热声理论所论述的热声功能,并指出交变流动斯特林热机进行的不是传统热力分析认为的两个等温过程和两个等容回热过程组成的斯特林循环。     

Power-Optimal Control of a Stirling Engine’s Frictional Piston Motion

The power output of Stirling engines can be optimized by several means. In this study, the focus is on potential performance improvements that can be achieved by optimizing the piston motion of an alpha-Stirling engine in the presence of dissipative processes, in particular mechanical friction. We use a low-effort endoreversible Stirling engine model, which allows for the incorporation of finite heat and mass transfer as well as the friction caused by the piston motion. Instead of performing a parameterization of the piston motion and optimizing these parameters, we here use an indirect iterative gradient method that is based on Pontryagin’s maximum principle. For the varying friction coefficient, the optimization results are compared to both, a harmonic piston motion and optimization results found in a previous study, where a parameterized piston motion had been used. Thus we show how much performance can be improved by using the more sophisticated and numerically more expensive iterative gradient method.     

Performance characteristic of a Stirling refrigeration cycle in micro/nano scale

The aim of the paper is to present the performance characteristics of a Stirling refrigeration cycle in micro/nano scale, in which the working substance of cycle is an ideal Maxwellian gas. Due to the quantum boundary effect on the gas particles confined in the finite domain, the cycle no longer possesses the condition of perfect regeneration. The inherent regenerative losses, the refrigeration heat and coefficient of performance (COP) of the cycle are derived. It is found that, for the micro/nano scaled Stirling refrigeration cycle devices, the refrigeration heat and COP of cycle all depend on the surface area of the system (boundary of cycle) besides the temperature of the heat reservoirs, the volume of system and other parameters, while for the macro scaled refrigeration cycle devices, the refrigeration heat and COP of cycle are independent of the surface area of the system. Variations of the refrigeration heat ratio r_R and the COP ratio r_ε with the temperature ratio τ and volume ratio r_V for the different surface area ratio r_A are examined, which reveals the influence of the boundary of cycle on the performance of a micro/nano scaled Stirling refrigeration cycle. The results are useful for designing of a micro/nano scaled Stirling cycle device and may conduce to confirming experimentally the quantum boundary effect in the micro/nano scaled devices.     

Maximum obtainable specific power of high-temperature waste heat engines

An endoreversible Carnot cycle is presented in this paper for a heat engine using higt-temperature waste heat. The endoreversible Carnot cycle is a modified Carnot cycle, where the heat-transferred between the heat engine and its surroundings is the only irreversible process. Since the energy input (waste heat) to the heat engine is free, the cost of the output power of the heat engine depends mainly on the size of the heat exchangers. A specific power, power per unit area of heat exchanger surface area, is adopted as the objective function for the performance analysis of the heat engine. The relation between the maximum obtainable specific power and the temperature range in which the high-temperature waste heat engine operates is found.     

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.     

Action and Entropy in Heat Engines: An Action Revision of the Carnot Cycle

Despite the remarkable success of Carnot’s heat engine cycle in founding the discipline of thermodynamics two centuries ago, false viewpoints of his use of the caloric theory in the cycle linger, limiting his legacy. An action revision of the Carnot cycle can correct this, showing that the heat flow powering external mechanical work is compensated internally with configurational changes in the thermodynamic or Gibbs potential of the working fluid, differing in each stage of the cycle quantified by Carnot as caloric. Action (@) is a property of state having the same physical dimensions as angular momentum (mrv = mr²ω). However, this property is scalar rather than vectorial, including a dimensionless phase angle (@ = mr²ωδφ). We have recently confirmed with atmospheric gases that their entropy is a logarithmic function of the relative vibrational, rotational, and translational action ratios with Planck’s quantum of action ħ. The Carnot principle shows that the maximum rate of work (puissance motrice) possible from the reversible cycle is controlled by the difference in temperature of the hot source and the cold sink: the colder the better. This temperature difference between the source and the sink also controls the isothermal variations of the Gibbs potential of the working fluid, which Carnot identified as reversible temperature-dependent but unequal caloric exchanges. Importantly, the engine’s inertia ensures that heat from work performed adiabatically in the expansion phase is all restored to the working fluid during the adiabatic recompression, less the net work performed. This allows both the energy and the thermodynamic potential to return to the same values at the beginning of each cycle, which is a point strongly emphasized by Carnot. Our action revision equates Carnot’s calorique, or the non-sensible heat later described by Clausius as ‘work-heat’, exclusively to negative Gibbs energy (−G) or quantum field energy. This action field complements the sensible energy or vis-viva heat as molecular kinetic motion, and its recognition should have significance for designing more efficient heat engines or better understanding of the heat engine powering the Earth’s climates.     

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.     

Thermoeconomic analysis of an irreversible Stirling heat pump cycle

In this paper an analysis of the Stirling cycle in thermoeconomic terms is developed using the entropy generation. In the thermoeconomic optimization of an irreversible Stirling heat pump cycle the F function has been introduced to evaluate the optimum for the higher and lower sources temperature ratio in the cycle: this ratio represents the value which optimizes the cycle itself. The variation of the function F is proportional to the variation of the entropy generation, the maxima and minima of F has been evaluated in a previous paper without giving the physical foundation of the method. We investigate the groundwork of this approach: to study the upper and lower limits of F function allows to determine the cycle stability and the optimization conditions. The optimization consists in the best COP at the least cost. The principle of maximum variation for the entropy generation becomes the analytic foundation of the optimization method in the thermoeconomic analysis for an irreversible Stirling heat pump cycle.     

Performance characteristics and parametric optimization of an irreversible magnetic Ericsson heat-pump

Taking into account the finite-rate heat transfer in the heat-transfer processes, heat leak between the two external heat reservoirs, regenerative loss, regeneration time, and internal irreversibility due to dissipation of the cycle working substance, an irreversible magnetic Ericsson heat-pump cycle is presented. On the basis of the thermodynamic properties of magnetic materials, the performance characteristics of the irreversible magnetic Ericsson heat-pump are investigated and the relationship between the optimal heating load and the coefficient of performance (COP) is derived. Moreover, the maximum heating load and the corresponding COP as well as the maximum COP and the corresponding heating load are obtained. Furthermore, the other optimal performance characteristics are discussed in detail. The results obtained here may provide some new information for the optimal parameter design and the development of real magnetic Ericsson heat-pumps.     

燃气驱动热声发动机中加热器的设计与实验验证

加热器在热声发动机的能量传递和转化过程中起着重要作用,是热声发动机的核心部件之一。目前热声发动机大多采用电能驱动,采用燃气直接燃烧驱动将对热声发动机的实用化具有积极促进意义。根据热声发动机的工作特点,以时均流对流换热公式为依据,设计了一种新型燃气燃烧驱动加热器,并应用于现有的混合型热声发动机实验台上,取得了较好的实验结果。