An analysis of beta type Stirling engine with rhombic drive mechanism

Stirling engine system is one of the options for electrifying a remote community not serviceable by the grid, which can operate on energy input in the form of heat. Major hurdle for the wide-spread usage of rhombic drive beta type Stirling engine is complexity of the drive and requirement of tight tolerances for its proper functioning. However, if the operating and geometrical constraints of the system are accounted for, different feasible design options can be identified. In the present work, various aspects that need to be considered at different decision making stages of the design and development of a Stirling engine are addressed. The proposed design methodology can generate and evaluate a range of possible design alternatives which can speed up the decision making process and also provide a clear understanding of the system design considerations. The present work is mainly about the design methodology for beta type Stirling engine and the optimization of phase angle, considering the effect of overlapping volume between compression and expansion spaces. It is also noticed that variation of compression space volume with phase angle remains sinusoidal for any phase difference. The aim of the present work is to find a feasible solution which should lead to a design of a single cylinder, beta type Stirling engine of 1.5 kW_e capacity for rural electrification.     

Theoretical limits on the performance of stirling engines

This paper describes a mathematical model of engines operating with an ideal Stirling cycle and subject to limited heat transfer, internal thermal losses, and mechanical friction losses. The goal of the paper is to describe the fundamental effects of these imperfections on the performance of an otherwise ideal Stirling engine. These are defects suffered by all real Stirling engines, but the intent here is not to predict the actual performance of specific engines. Rather, the aim is to obtain some mathematical insight into the nature of the theoretical dependence of engine performance upon these imperfections. © 1998 John Wiley & Sons, Ltd.     

以Dieterici气体为工质的两类热机循环性能分析

对Dieterici实际气体作了简要分析,并以Dieterici实际气体为工质,分别导出卡诺热机和斯特林热机的输出功和效率的一般表达式.最后通过数值计算,讨论了卡诺热机及斯特林热机的输出功和效率分别与体积和温度之间的关系.所得结论可为热机的运行条件和优化设计提供理论参考.     

Optimum Stirling engine geometry

This paper combines the author's work on mechanical efficiency of reciprocating engines with the classic Schmidt thermodynamic model for Stirling engines and revisits the problem of identifying optimal engine geometry. All previous optimizations using the Schmidt theory focused on obtaining a maximal specific indicated cyclic work. This does not necessarily produce the highest shaft output. Indeed, some optima based upon indicated work would yield engines that cannot run at all due to excessive intrinsic mechanical losses. The analysis presented in this paper shows how to optimize for shaft or brake work output. Specifically, it presents solutions to the problem of finding the piston‐to‐displacer swept volume ratio and phase angle which will give the maximum brake output for a given total swept volume, given temperature extremes, a given mean operating pressure, and a given engine mechanism effectiveness. The paper covers the split‐cylinder or gamma‐type Stirling in detail, serving as a model for similar analysis of the other Stirling engine configurations. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

The investigation of the effect of thermal barrier coating on the performance of Stirling engine

The shuttle heat transfer is one of the reasons reducing the performance of Stirling engines. This study is concerned with the reduction in shuttle heat transfer by coating the displacer. The displacer of a gamma type Stirling engine was coated with a layer of yttria‐stabilized zirconia (YSZ), and the effect of the coating on the engine performance was evaluated by comparing speed‐power and speed‐torque characteristics of the engine with coated and uncoated displacers. Characteristics were obtained for 700, 800 and 900°C heater temperatures. At each stage of the heater temperature, the charge pressure ranged from 1 to 3.5 bars with 0.5 bar increments. At 900°C heater temperature and 3 bars charge pressure, the shaft power before coating was 34.9 W, after coating the power increased to 43.8 W, which corresponds to a 25% increment. The temperature applied to the engine did not cause any damage on the coating layer. Copyright © 2008 John Wiley & Sons, Ltd.     

斯特林发动机管式加热器内振荡流动的换热特性实验研究

模拟管式加热器在斯特林发动机中的工作状态,研究加热器管内工作气体振荡流动的换热特性,得到气体压力、振荡频率等对换热的影响规律,进一步得到工作气体与管壁间的平均换热系数,并将结果转化为无量纲参数,比较稳定流动换热关联式计算结果与实验结果的偏差。实验结果可对斯特林发动机管式加热器设计、优化和换热性能预测提供参考。     

Similarity design and experimental investigation of a beta‐type Stirling engine with a rhombic drive mechanism

Stirling engines are power machines that operate over a closed, regenerative thermodynamic cycle with the ability to use any heat source from the outside, including hydrogen, solar energy, and biomass fuels. In this work, the development of a beta‐type Stirling engine is presented. The improved similarity design and optimization methods are described in detail, as are the key parameters of the constructed prototype and the arrangement of the entire test rig. A new structure for the expansion exchangers is developed to reduce the flow loss. The performance test of the prototype engine is conducted under laboratory conditions using an electrical heating system. In this test, the temperature and the pressure of the working fluid are monitored by thermocouples and pressure sensors, respectively. The speed and the torque of the output shaft are obtained by the dynamometer. Finally, the preliminary test results with the prototype engine are shown. The maximum output shaft power can reach 288 W at 600°C and 15‐bar charge pressure. Copyright © 2014 John Wiley & Sons, Ltd.     

The effect of the overall heat transfer coefficient variation on the optimal distribution of the heat transfer surface conductance or area in a Stirling engine

This study aims to assess for a Stirling engine the influence of the overall heat transfer coefficient variation on the optimum state and on the optimum distribution of the heat transfer surface conductance or area among the machine heat exchangers. The analysis is based on a Stirling machine optimization method, previously elaborated, which is now applied to a cycle with total heat regeneration. The method was conceived for an irreversible cycle with heat transfer across temperature differences at the source and the sink, and heat losses between the hot-end and the cold-end of the engine. Source and sink of finite thermal capacity as well as thermostats are considered. The new approach considers a linear variation of the overall heat transfer coefficient of the machine heat exchangers with respect to the local temperature difference. A comparison of the optimum state and the optimum distribution of the heat transfer surface conductance or area among the heater and the cooler is made for several cases.     

Mobile hydraulic power supply: Liquid piston Stirling engine pump

Conventional mobile hydraulic power supplies involve numerous kinematic connections and are limited by the efficiency, noise, and emissions of internal combustion engines. The Stirling cycle possesses numerous benefits such as the ability to operate from any heat source, quiet operation, and high theoretical efficiency. The Stirling engine has seen limited success due to poor heat transfer in the working chambers, difficulty sealing low-molecular weight gases at high pressure, and non-ideal piston displacement profiles. As a solution to these limitations, a liquid piston Stirling engine pump is proposed. The liquid pistons conform to irregular volumes, allowing increased heat transfer through geometry features on the interior of the working chambers. Creating near-isothermal operation eliminates the costly external heat exchangers and increases the engine efficiency through decreasing the engine dead space. The liquid pistons provide a positive gas seal and thermal transport to the working chambers. Controlling the flow of the liquid pistons with valves enables matching the ideal Stirling cycle and creates a direct hydraulic power supply. Using liquid hydrogen as a fuel source allows cooling the compression side of the engine before expanded the fuel into a gas and combusting it to heat the expansion side of the engine. Cooling the compression side not only increases the engine power, but also significantly increases the potential thermal efficiency of the engine. A high efficiency Stirling engine makes energy regeneration through reversing the Stirling cycle practical. When used for regeneration, the captured energy can be stored in thermal batteries, such as a molten salt. The liquid piston Stirling engine pump requires further research in numerous areas such as understanding the behavior of the liquid pistons, modeling and optimization of a full engine pump, and careful selection of materials for the extreme operating temperatures. Addressing these obtainable research quandaries will enable a transformative Stirling engine pump with the potential to excel in numerous applications.     

Free piston Stirling engines: A review

This paper presents a detailed review on free piston Stirling engines (FPSEs) technology. Generally, the Stirling engines can be categorized into two broad classes comprising kinematic and dynamic converters among which FPSEs are known as the dynamic type. Other well-known dynamic Stirling converters are Fluidyne and thermosacoustic engines among which the thermosacoustic ones are the most advanced Stirling converters recently presented. In this research, the dynamic Stirling engines are first introduced and reviewed. Then, the review work is directed toward the FPSEs, one of the most reliable dynamic Stirling converters utilized in different applications such as combined heat and power systems (CHPs). Subsequently, the working principles of different types of FPSEs and their performance are summarized. Next, several manufactured FPSEs, as well as their corresponding features and applications, are discussed. Finally, the article is conducted to analysis and modeling approaches of FPSEs. Accordingly, linear and nonlinear analytical techniques of FPSEs are introduced, and some comparative data are provided to verify the modeling schemes. Then, various design parameters affecting the engine performance are introduced and studied. The outcomes of this review work demonstrate the potential of FPSEs for different applications and reveal that the perturbation-based model is likely the most comprehensive nonlinear method for modeling and design of the FPSEs.     

Design considerations for a power optimized regenerative endoreversible Stirling cycle

An evaluation of the major theoretical considerations concerning the design of an endoreversible Stirling cycle with ideal regeneration is given. The factors affecting optimum power and efficiency at optimum power are analysed for the cycle based upon higher and lower temperature bounds. Heat transfer characteristics of the regenerator and the thermal source and sink, individual process times for the cycle have been studied with respect to engine design parameters like speed, compression ratio, etc. The results of this study provide additional information for use in the optimized design and evaluation of Stirling engines. Copyright © 2000 John Wiley & Sons, Ltd.     

SIZE LIMITS FOR REGENERATIVE HEAT ENGINES

This article explores the lower size limit placed on regenerative heat engines by thermodynamics and heat transfer. Information derived in this work has direct relevance to the development of mesoscopic heat engines that are based on standard gas cycles employing regeneration. A model is developed for the Stirling cycle that incorporates a regenerator effectiveness term and an axial conduction term, both of which are dependent on the length scale of the device. The thermal efficiency for the engine is determined in terms of the cycle temperature ratio, the expansion ratio, regenerator effectiveness, and a nondimensional term called the conduction parameter. Results from this study show that a small-scale heat engine fabricated from a low-thermal-conductivity material can be made with a length scale approaching 1 mm. Such a device would undoubtedly be composed of numerous microscale components. Below the 1-mm limit, efficiency suffers to such a degree that solid-state thermoelectric devices would become a better choice for a particular application.     

Efficiency bound of a solar-driven stirling heat engine system

A solar-driven Stirling engine is modelled as a combined system which consists of a solar collector and a Stirling engine. The performance of the system is investigated, based on the linearized heat loss model of the solar collector and the irreverisible cycle model of the Stirling engine affected by finite-rate heat transfer and regenerative losses. The maximum efficiency of the system and the optimal operating temperature of the solar collector are determined. Moreover, it is pointed out that the investigation method in the present paper is valid for other heat loss models of the solar collector as well, and the results obtained are also valid for a solar-driven Ericsson engine system using an ideal gas as its engine work substance. © 1998 John Wiley & Sons, Ltd.     

Energy, exergy and cost analysis of a micro-cogeneration system based on an Ericsson engine

Hot air engines (Stirling and Ericsson engines) are well suited for micro-cogeneration applications because they are noiseless, and they require very low maintenance. Ericsson engines (i.e. Joule cycle reciprocating engines with external heat supply) are especially interesting because their design is less constrained than Stirling engines, leading to potentially cheaper and energetically better systems. We study the coupling of such an Ericsson engine with a system of natural gas combustion. In order to design this plant, we carry out classic energy, exergy and exergo-economic analyses. This study does not deal with a purely theoretical thermodynamic cycle. Instead, it is led with a special attempt to describe as accurately as possible what could be the design and the performance of a real engine. It allows us to balance energetic performance and heat exchanger sizes, to plot the exergy Grassmann diagram, and to evaluate the cost of the thermal and electric energy production. These simple analyses confirm the interest of such systems for micro-cogeneration purposes. The main result of this study is thus to draw the attention on Ericsson engines, unfortunately unfairly fallen into oblivion.     

Thermodynamic analysis of a Stirling engine including dead volumes of hot space, cold space and regenerator

This paper provides a theoretical investigation on the thermodynamic analysis of a Stirling engine. An isothermal model is developed for an imperfect regeneration Stirling engine with dead volumes of hot space, cold space and regenerator that the regenerator effective temperature is an arithmetic mean of the heater and cooler temperature. Numerical simulation is performed and the effects of the regenerator effectiveness and dead volumes are studied. Results from this study indicate that the engine net work is affected by only the dead volumes while the heat input and engine efficiency are affected by both the regenerator effectiveness and dead volumes. The engine net work decreases with increasing dead volume. The heat input increases with increasing dead volume and decreasing regenerator effectiveness. The engine efficiency decreases with increasing dead volume and decreasing regenerator effectiveness.     

Optimization of Output Power and Thermal Efficiency of Solar‐Dish Stirling Engine Using Finite Time Thermodynamic Analysis

This paper presents an investigation on finite time thermodynamic (FTT) evaluation of a solar‐dish Stirling heat engine. FTTs has been applied to determine the output power and the corresponding thermal efficiency, exergetic efficiency, and the rate of entropy generation of a solar Stirling system with a finite rate of heat transfer, regenerative heat loss, conductive thermal bridging loss, and finite regeneration process time. Further imperfect performance of the dish collector and convective/radiative heat transfer mechanisms in the hot end as well as the convective heat transfer in the heat sink of the engine are considered in the developed model. The output power of the engine is maximized while the highest temperature of the engine is considered as a design parameter. In addition, thermal efficiency, exergetic efficiency, and the rate of entropy generation corresponding to the optimum value of the output power is evaluated. Results imply that the optimized absorber temperature is some where between 850 K and 1000 K. Sensitivity of results against variations of the system parameters are studied in detail. The present analysis provides a good theoretical guidance for the designing of dish collectors and operating the Stirling heat engine system.     

斯特林热机的性能优化分析

考虑了斯特林热机工作过程中热阻的不可逆性、等容回热过程的有限时间性以及回热损失,应用有限时间热力学理论,对牛顿传热机的性能进行了优化分析,得到了对优化设计,最佳工作参数选择有意义的结论。     

新型回热器结构设计及换热特性研究

回热器作为斯特林热机的关键部件,对于太阳能斯特林热机整机性能有着重要影响。为克服传统金属丝网回热器结构存在的填料单一,制造成本较高,工艺复杂问题,采用实用等温分析法,以回热器的长径比、通流面积、填料种类以及孔隙率各项回热器参数为基础,设计了一种新型斯特林热机回热器,该回热器具有轴向压降小,换热性能高,结构稳定,加工制造简单的特点。开展了新型回热器和传统金属丝网回热器的换热性能对比研究,采用振荡条件下的局部热平衡方法研究回热器的传热过程,对比传统金属丝网回热器和新型回热器的温度变化,速度变化以及压力变化。结果表明:在整体孔隙率相同的条件下,新型回热器和传统金属丝网回热器相比,整体启动速率相似,但新型回热器压降减少0.04 MPa,速度出现分段式变化,有利于回热器的换热和结构稳定。因此,新型回热器不但在结构上优于传统金属丝网回热器,在换热特性上也优于传统金属丝网回热器。     

1.2 kW beta type Stirling engine with rhombic drive mechanism

Because of some advantages such as higher theoretical thermal efficiency, lower pollutant release, working with lower noisy, working with any kind of thermal energy, and having longer life time, Stirling engines receive attentions of academic workers. The development studies related to the drive mechanism as well as the other components of Stirling engine are progressing. In the present study, a beta type Stirling engine with a rhombic‐drive mechanism was manufactured and tested. Tests were performed at hot end temperatures of 600 and 800°C for five different stages of charge pressure ranging from 1 to 5 bar with 1 bar increments. Torque and power characteristics of the engine were deduced. The maximum engine torque and power were obtained as 18 Nm and 1215 W at engine speeds of 612 and 722 rpm, respectively, at 4 bar charging pressure. The cyclic work generations of the engine, which is an important parameter indicating the engine performance, were determined as 19, 27, and 25 J corresponding to 1, 3, and 5 bar charging pressures, respectively. In the experiments, the cylinder pressure variation was also measured at various charging pressures. While the charge pressure increases from 1 to 5 bar, the location of the maximum cylinder pressure ranged from 86° to 74° of crankshaft angle, which may have a bit influence on the engine performance. Copyright © 2017 John Wiley & Sons, Ltd.