The effect of displacer material on the performance of a low temperature differential Stirling engine

In this study, a gamma‐type low temperature differential Stirling engine was designed and manufactured. The displacer and piston of the engine were concentrically situated to each other. The engine was tested by using a liquefied petroleum gas burner at laboratory conditions. The working fluid was ambient air at atmospheric pressure. Test procedure intended to investigate the speed‐torque and speed‐power characteristics of the engine depending on the hot‐end temperature. Two different displacers made of aluminum alloy and medium density fiberboard were used. The maximum torque and power obtained were 0.166 Nm at 125 rpm speed and 3.06 W at 215 rpm speed, respectively, at 160 °C hot‐end temperature with medium density fiberboard displacer. Copyright © 2011 John Wiley & Sons, Ltd.     

Gas dynamic characteristic of displacer in Stirling cryocoolers

Based on the vector analysis of the dynamic characteristic of the displacer in split-type Stirling cryocoolers, experimental study was performed on a 2 W@80 K cooler to uncover the relationship among pressure fluctuation, damped impedance, inherent frequency, cold-tip temperature and the cooling performance. The result shows that the pressure amplitude and phase shift between pressure and displacer motion decrease when the cooling temperature decreases; the dynamic damp of the displacer increases at lower cooling temperature, which results in the increase of pressure drop of the regenerator, the decrease of average pressure of the cold cubage, the decrease of gas dynamic pressure, the decrease of phase shift between pressure and displacer motion, and the displacement of the regenerator and the PV power; at lower cooling temperature, the inherent frequency of the displacer increases because of the augmentation of gas spring constant. And as the inherent frequency is getting closer to the operating frequency, the drive current of the motor decreases; the piston of the compressor affects the displacer by the pressure fluctuation engendered by its motion, and the displacer reacts by changing the mass and momentum distribution to adjust the gas spring constant and the damp coefficient.     

An experimental study on the development of a β-type Stirling engine for low and moderate temperature heat sources

In this study, a β-type Stirling engine was designed and manufactured which works at relatively lower temperatures. To increase the heat transfer area, the inner surface of the displacer cylinder was augmented by means of growing spanwise slots. To perform a better approach to the theoretical Stirling cycle, the motion of displacer was governed by a lever. The engine block was used as pressurized working fluid reservoir. The escape of working fluid, through the end-pin bearing of crankshaft, was prevented by means of adapting an oil pool around the end-pin. Experimental results presented in this paper were obtained by testing the engine with air as working fluid. The hot end of the displacer cylinder was heated with a LPG flame and kept about 200 °C constant temperature throughout the testing period. The other end of the displacer cylinder was cooled with a water circulation having 27 °C temperature. Starting from ambient pressure, the engine was tested at several charge pressures up to 4.6 bars. Maximum power output was obtained at 2.8 bars charge pressure as 51.93 W at 453 rpm engine speed. The maximum torque was obtained as 1.17 Nm at 2.8 bars charge pressure. By comparing experimental work with theoretical work calculated by nodal analysis, the convective heat transfer coefficient at working fluid side of the displacer cylinder was predicted as 447 W/m² K for air. At maximum shaft power, the internal thermal efficiency of the engine was predicted as 15%.     

Gas dynamic characteristic of displacer in Stirling cryocoolers

Based on the vector analysis of the dynamic characteristic of the displacer in split-type Stirling cryocoolers, experimental study was performed on a 2 W@80 K cooler to uncover the relationship among pressure fluctuation, damped impedance, inherent frequency, cold-tip temperature and the cooling performance. The result shows that the pressure amplitude and phase shift between pressure and displacer motion decrease when the cooling temperature decreases; the dynamic damp of the displacer increases at lower cooling temperature, which results in the increase of pressure drop of the regenerator, the decrease of average pressure of the cold cubage, the decrease of gas dynamic pressure, the decrease of phase shift between pressure and displacer motion, and the displacement of the regenerator and the PV power; at lower cooling temperature, the inherent frequency of the displacer increases because of the augmentation of gas spring constant. And as the inherent frequency is getting closer to the operating frequency, the drive current of the motor decreases; the piston of the compressor affects the displacer by the pressure fluctuation engendered by its motion, and the displacer reacts by changing the mass and momentum distribution to adjust the gas spring constant and the damp coefficient. __________ Translated from Cryogenics, 2007, 159(5): 10–14 [译自: 低温工程]     

Motion characteristic of a free piston linear engine

A mathematical model of a free piston linear engine is established. The motion characteristics as well as the natural frequency map of the free piston are established. Then, its motion characteristics are successfully explained from the oscillation point. The full simulation model is built up in Matlab/Simulink for a better understanding of its motion features. The results show that the free piston system is a forced vibration system with variable damping coefficient and stiffness. Its steady-state response of periodical excitation is convergent which means that the system is stable under the periodical combustion. Furthermore, it has some unique features which are different from those of traditional Internal Combustion (IC) engines.     

Dynamic simulation of a beta-type Stirling engine with cam-drive mechanism via the combination of the thermodynamic and dynamic models

Dynamic simulation of a beta-type Stirling engine with cam-drive mechanism used in concentrating solar power system has been performed. A dynamic model of the mechanism is developed and then incorporated with the thermodynamic model so as to predict the transient behavior of the engine in the hot-start period. In this study, the engine is started from an initial rotational speed. The torques exerted by the flywheel of the engine at any time instant can be calculated by the dynamic model as long as the gas pressures in the chambers, the mass inertia, the friction force, and the external load have been evaluated. The instantaneous rotation speed of the engine is then determined by integration of the equation of rotational motion with respect to time, which in return affects the instantaneous variations in pressure and other thermodynamic properties of the gas inside the chambers. Therefore, the transient variations in gas properties inside the engine chambers and the dynamic behavior of the engine mechanism should be handled simultaneously via the coupling of the thermodynamic and dynamic models. An extensive parametric study of the effects of different operating and geometrical parameters has been performed, and results regarding the effects of mass moment of inertia of the flywheel, initial rotational speed, initial charged pressure, heat source temperature, phase angle, gap size, displacer length, and piston stroke on the engine transient behavior are investigated.     

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.     

Torque and power characteristics of a helium charged Stirling engine with a lever controlled displacer driving mechanism

This study presents test results of a Stirling engine with a lever controlled displacer driving mechanism. Tests were conducted with helium and the working fluid was charged into the engine block. The engine was loaded by means of a prony type micro dynamometer. The heat was supplied by a liquefied petroleum gas (LPG) burner. The engine started to run at 118 °C hot end temperature and the systematic tests of the engine were conducted at 180 °C, 220 °C and 260 °C hot end external surface temperatures. During the test, cold end temperature was kept at 27 °C by means of water circulation. Variation of the shaft torque and power with respect to the charge pressure and hot end temperature were examined. The maximum torque and power were measured as 3.99 Nm and 183 W at 4 bars charge pressure and 260 °C hot end temperature. Maximum power corresponded to 600 rpm speed.     

Numerical prediction of performance of a low-temperature-differential gamma-type Stirling engine

Abstract

In this study, a numerical simulation model is used to analyze thermodynamic performance of a low temperature-differential gamma-type Stirling engine by adjusting some values of the operating and geometrical parameters around a designated baseline case. The influences of these operating and geometrical parameters on engine performance such as working fluid materials, the stroke of piston and displacer, charged pressure, the heating temperature, and so on, are concerned. A numerical simulation model is established based on turbulent flow assumption and the realizable k – ε model is employed to solve the flow and thermal fields in the engine. In regard to flow in regenerator, Darcy–Forchheimer model was used to depict dynamic behavior of working fluid. Besides, thermal equilibrium model was used for solving the energy equation. Finally, working fluid in the engine undergoes a wide range of pressure and temperature so the effects of temperature and pressure on the viscosity and thermal conductivity of the working fluid are required to include. Thermal conductivity of porous medium matrix is affected by wide range of temperature as well.     

小型斯特林发动机不同外加热工况下运行的探索性实验

该文就其微型化可能产生的一系列问题,如：输出频率过高、产生转矩过小、冷热端差过小等进行了分析。提出自由活塞式斯特林发动机比热声式更具微型化的优势。并对一台长12cm、直径2．5cm的小型活塞式斯特林发动机进行了实验。实验中发动机热端温度范围64～626℃,通过测量其外壁面温度和声信号随时问的变化,得到发动机的稳定性和输出功率随外加热功率变化规律。该发动机的理论最高功率密度为102kW／m^3。     

自由活塞斯特林机动子运动阻尼特性研究

为准确描述自由活塞斯特林机动子的动力学特性,将黏性阻尼与库伦阻尼的分离计算法引入动子的运动阻尼分析中。通过理论分析和实验验证,并与等效黏性阻尼计算法进行对比,证明了分离计算法的正确性和实用性。研究结果表明：动子在往复运动中的接触摩擦与常规接触摩擦不同,其阻尼力既不只是一个定常摩擦力,也不只是速度的线性函数,而是由于往复运动,动子的局部接触情况随位移发生变化,表现为与位置相关的摩擦力。因此,动子往复运动中的阻尼特性应采用一个黏性阻尼系数与一个定常摩擦力共同描述。     

斯特林发动机在空间太阳能发电中的应用

提出了空间太阳能发电系统中采用自由活塞式期特林发动机发电装置的概念设计模型,确立了整个概念设计的框架,并对自由活塞式斯特林发动机作了初步设计,同时对有关问题进行了讨论,提示了今后的发展方向。     

Improved Stirling engine performance through displacer surface treatment

This study intended to improve the performance of the beta‐type Stirling engine, being developed by the authors for solar energy and low‐grade heat sources, by means of displacer surface treatments. Three different displacers were manufactured and tested where one of them was without any surface treatment, other was zirconium coated with 0.15 mm thickness, and the other was helically knurled with 0.30 mm track depth. Because of good thermo‐physical properties, helium was used as the working fluid. The heat was supplied by an LPG burner. Tests were conducted at 360±10°C hot end temperature. The highest engine power was obtained with knurled displacer as 250 W at 545 rpm speed and corresponding to this power 4.38 Nm torque was obtained. This was followed by coated and smooth displacers. Power increments provided by the knurled displacer are 40 and 60% compared with the zirconium‐coated and untreated displacers. Increments of knurled displacer's torque compared with that of coated and untreated displacers are 13 and 30%, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

Thermodynamic analysis of rhombic-driven and crank-driven beta-type Stirling engines

This work aims to compare beta-type Stirling engine performance (GPU-3 [ground power unit]) driven by rhombic and crank mechanisms. A modified non-ideal adiabatic model accounting for different frictional and thermal losses was adopted in this study. After validating the current model with engine experimental data, different scenarios of operating conditions including heater temperature, cooler temperature, charge pressure and engine speed were investigated. The results revealed that rhombic drive mechanism generates 32% more power and provides 20% more efficiency than crank mechanism at normal operating conditions. However, at low hot end temperature (300°C) and high charge pressure (50 bar) crank drive mechanism tends to slightly generate power more than rhombic drive mechanism at lower engine speeds. At low hot end temperature (300°C) and charge pressure (10 bar) both mechanisms cannot deliver any positive power. Higher power loss is recognized in crank drive mechanism at higher speeds due to increased pumping and gas spring hysteresis losses. This study highlights a wide analysis opportunity for designers and researchers of GPU-3 Stirling engine for further optimization.     

斯特林发动机V型传动系统激励力的计算分析研究

介绍了有关斯特林发动机传动系统激励力的计算分析研究。建立了斯特林发动机传动系统刚柔混合的多体动力学模型,计算了曲轴主轴承载荷和活塞侧推力等激励力。对比分析了有、无齿轮啮合力对主轴承载荷的影响,指出:计算斯特林发动机传动系统激励力时应考虑齿轮啮合冲击力的影响。对比分析了不同活塞间隙对活塞侧推力的影响,结果表明:活塞杆与缸套间隙在0.08~0.12 mm时,活塞侧推力的影响较小。     

Simulation, construction and testing of a two-cylinder solar Stirling engine powered by a flat-plate solar collector without regenerator

In this research, a gamma-type, low-temperature differential (LTD) solar Stirling engine with two cylinders was modeled, constructed and primarily tested. A flat-plate solar collector was employed as an in-built heat source, thus the system design was based on a temperature difference of 80 °C. The principles of thermodynamics as well as Schmidt theory were adapted to use for modeling the engine. To simulate the system some computer programs were written to analyze the models and the optimized parameters of the engine design were determined. The optimized compression ratio was computed to be 12.5 for solar application according to the mean collector temperature of 100 °C and sink temperature of 20 °C. The corresponding theoretical efficiency of the engine for the mentioned designed parameters was calculated to be 0.012 for zero regenerator efficiency. Proposed engine dimensions are as follows: power piston stroke 0.044 m, power piston diameter 0.13 m, displacer stroke 0.055 m and the displacer diameter 0.41 m. Finally, the engine was tested. The results indicated that at mean collector temperature of 110 °C and sink temperature of 25 °C, the engine produced a maximum brake power of 0.27 W at 14 rpm. The mean engine speed was about 30 rpm at solar radiation intensity of 900 W/m² and without load. The indicated power was computed to be 1.2 W at 30 rpm.     

Performance of a beta-configuration heat engine having a regenerative displacer

This paper investigates the performance of a beta-configuration heat engine having a regenerative displacer. In the conventional beta-engine; the displacer and the power piston are incorporated in one cylinder. The displacer transfers the working fluid between expansion and compression spaces via the heater, the regenerator, and the cooler. In the present work, successive homogeneous layers of square wire meshes occupy the displacer space of a beta-engine that make the displacer to be a displacer and a regenerator simultaneously. The theoretical analysis of the engine is based mainly on Schmidt theory. The optimum dimensions of the heater, cooler, regenerator, piston stroke and displacer stroke as dimensionless ratios of the bore were found. The optimum phase angle between the piston and the displacer and the optimum ranges of the speed for each working gas were also found. In a comparison between the proposed engine which has a regenerative displacer and the GPU-3 engine which has a stationary regenerator and a solid displacer; it was found that; the proposed one delivers 20% more power with 10% more efficiency than the GPU-3 engine.     

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.     

Field-test of a solar low delta-T Stirling engine

The ultimate aim of a Moroccan–German study is to develop a simple solar pumping system, using the concept of low delta-T Stirling engines. This paper describes the main parts of the engine and presents several experimental measurements made under laboratory and field-test conditions in Morocco. Measurements with flat plate cooler and discontinuous motion of the displacer were conducted to verify two essential recommendations of Kolin in expectation of power-output improvements of the gamma-type engine.     

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.