Analysis of the stirling heat engine at maximum power conditions

The Stirling heat engine operating in a closed regenerative thermodynamic cycle is analyzed. Polytropic processes are used for the power and displacement pistons. Following regeneration, the maximum power density and efficiency are found and the compression ratio at maximum power density is determined.     

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。     

Study of a Stirling engine used for domestic micro‐cogeneration. Thermodynamic analysis and experiment

One of the aims of this work is the study of the geometry of a micro‐cogenerator using a Stirling engine with four double effect pistons. The complex geometry of the heat exchangers was determined by optical measurements. Results of three thermodynamic models: Direct Method from Finite Speed Thermodynamics (FST), isothermal model (Schmidt), and adiabatic model (Finkelstein) are confronted to experimental ones. Direct Method consists of the study and the evaluation of the irreversibilities of thermal machines by analyzing the cycle, step by step, and directly integrating the equation of the First Law for processes with finite speed combined with Second Law of Thermodynamics, for each process of the cycle. The expression of efficiency and power, depending on the speed of the processes and geometric and functional parameters, is then obtained in a straightforward manner. The isothermal and adiabatic models are based on the division of Stirling engine in 3, respectively 5 control volumes, for which the ideal gas law and the equations of mass and energy balance are applied. Analysis of the process of heat transfer and flow of the working gas, taking place in the Stirling engine, is carried out taking into account instantaneous representation of the working fluid volume in the engine. A system of differential equations is solved by iteration using Matlab/Simulink software. The theoretical results are compared to experimental ones. This comparison allows to point out a good accuracy of the Direct Method and the Adiabatic Model, for the thermal operating parameters of the system, noting the different assumptions of each analysis. Copyright © 2015 John Wiley & Sons, Ltd.     

Mathematical modelling of a hydraulic free-piston engine considering hydraulic valve dynamics

This paper describes the design of a single piston compression ignition hydraulic free-piston engine. An engine simulation model considering hydraulic valve dynamics is built. Extensive simulated results are presented and the major features of the engine are discussed. Experimental results from a full-cycle test of a prototype are also included and analysed integrated with simulation as well. The good agreement between experiments and simulations confirms the model can predict the engine performance. The engine takes more time in the suck phase for one cycle, which is helpful in sucking the low-pressure oil into the pump chamber. The dynamics of valves on the hydraulic chambers affect the chamber pressures. The pump chamber valve response lag compared with the piston displacement affects not only the chamber volumetric efficiency but also the engine fuel economy. The unchangeable piston motion trajectory makes the engine possible to get a high volumetric efficiency with fixed check valves. The rebound changes the compression stroke length and should be considered in the engine control. Asymmetric strokes appear when the engine is running under the piston self-excited vibration frequency.     

Performance of low-temperature differential Stirling engines

In this paper, two single-acting, twin power piston and four power pistons, gamma-configuration, low-temperature differential Stirling engine are designed and constructed. The engine performance is tested with air at atmospheric pressure by using a gas burner as a heat source. The engine is tested with various heat inputs. Variations of engine torque, shaft power and brake thermal efficiency at various heat inputs with engine speed and engine performance are presented. The Beale number obtained from testing of the engines is also investigated. The results indicate that, for twin power piston engine, at a maximum actual heat input of 2355 J/s with a heater temperature of 589 K, the engine produces a maximum torque of 1.222 N m at 67.7 rpm, a maximum shaft power of 11.8 W at 133 rpm, and a maximum brake thermal efficiency of 0.494% at 133 rpm, approximately. For the four power pistons engine, the results indicate that at the maximum actual heat input of 4041 J/s with the heater temperature of 771 K, the engine produces a maximum torque of 10.55 N m at 28.5 rpm, a maximum shaft power of 32.7 W at 42.1 rpm, and a maximum brake thermal efficiency of 0.809% at 42.1 rpm, approximately.     

Application of the multi-objective optimization method for designing a powered Stirling heat engine: Design with maximized power,thermal efficiency and minimized pressure loss

In the recent years, numerous studies have been done on Stirling cycle and Stirling engine which have been resulted in different output power and engine thermal efficiency analyses. Finite speed thermodynamic analysis is one of the most prominent ways which considers external irreversibilities. In the present study, output power and engine thermal efficiency are optimized and total pressure losses are minimized using NSGA algorithm and finite speed thermodynamic analysis. The results are successfully verified against experimental data.     

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.     

Performance of a twin power piston low temperature differential Stirling engine powered by a solar simulator

This paper provides an experimental investigation on the performance of a low-temperature differential Stirling engine. In this study, a twin power piston, gamma-configuration, low-temperature differential Stirling engine is tested with non-pressurized air by using a solar simulator as a heat source. The engine testing is performed with four different simulated solar intensities. Variations of engine torque, shaft power and brake thermal efficiency with engine speed and engine performance at various heat inputs are presented. The Beale number, obtained from the testing of the engine, is also investigated. The results indicate that at the maximum simulated solar intensity of 7145 W/m², or heat input of 261.9 J/s, with a heater temperature of 436 K, the engine produces a maximum torque of 0.352 N m at 23.8 rpm, a maximum shaft power of 1.69 W at 52.1 rpm, and a maximum brake thermal efficiency of 0.645% at 52.1 rpm, approximately.     

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。     

Dynamic analysis of a free piston Stirling engine working with closed and open thermodynamic cycles

In free piston Stirling engines the power generated by the engine is related to the length of the piston and displacer strokes. Length of strokes vary with respect to the hot end temperature, external load, charge pressure, rod diameter, stiffness of springs, masses of piston and displacer and static positions of the piston and displacer. When the length of displacer and piston strokes exceeds the estimated limits, some mechanical collisions occur between piston and displacer or displacer and cylinder. In this work, the dynamic model of a free piston Stirling engine working with closed and open thermodynamic cycles was derived and numerically solved for an optional pair of the piston and displacer masses. Safe ranges were investigated for the hot end temperature, charge pressure, damping coefficient of the piston motion, stiffness of the piston spring and area of the displacer rod. The stiffness of the displacer spring and static positions of the piston and displacer were optimized. Analysis indicated that, a free piston Stirling engine working with a closed thermodynamic cycle performs a stable operation within a small range of the hot end temperature and damping coefficient of the piston motion. By means of inverting the engine into an open-cycle engine, the limited range of the hot end temperature and the damping coefficient of the piston motion were partially enlarged.     

液压自由活塞发动机的能量平衡分析

液压自由活塞发动机是将一次动力机－内燃机与二次动力机－液压泵的集成为一体，以液体为工作介质，利用油液压力能来实现动力非刚性传输的复合发动机，针对稳态运转的液压自由活塞发动机，分析了其能量输入，耗散，分配及输出情况，给出了各能量组分所占的比例，并估算了活塞的最大运动速度和负载压力，为HFPE的结构设计，控制和效率提高指明方向。     

Continuous hydrino thermal power system

The specifics of a continuous hydrino reaction system design are presented. Heat from the hydrino reactions within individual cells provide both reactor power and the heat for regeneration of the reactants. These processes occur continuously and the power from each cell is constant. The conversion of thermal power to electrical power requires the use of a heat engine exploiting a cycle such as a Rankine, Brayton, Stirling, or steam-engine cycle. Due to the temperatures, economy goal, and efficiency, the Rankine cycle is the most practical and can produce electricity at 30–40% efficiency with a component capital cost of about $300 per kW electric. Conservatively, assuming a conversion efficiency of 25% the total cost with the addition of the boiler and chemical components is estimated at $1064 per kW electric.     

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.     

Using supercritical heat recovery process in Stirling engines for high thermal efficiency

Stirling engine, using a composite working fluid, such as two-component fluid: gaseous carrier and phase-change component and single multi-phase fluid as the working fluid is studied to get high thermal efficiency. In Stirling engine with a composite fluid, a thermodynamic supercritical heat recovery and heating process is proposed and demonstrated to improve the heat transfer of the heat regenerator and cooler of common gaseous Stirling engine. The criteria for the choice of the working fluids are also formulated.     

Optimization of solar-powered Stirling heat engine with finite-time thermodynamics

A mathematical model for the overall thermal efficiency of the solar-powered high temperature differential dish-Stirling engine with finite-rate heat transfer, regenerative heat losses, conductive thermal bridging losses and finite regeneration processes time is developed. The model takes into consideration the effect of the absorber temperature and the concentrating ratio on the thermal efficiency; radiation and convection heat transfer between the absorber and the working fluid as well as convection heat transfer between the heat sink and the working fluid. The results show that the optimized absorber temperature and concentrating ratio are at about 1100 K and 1300, respectively. The thermal efficiency at optimized condition is about 34%, which is not far away from the corresponding Carnot efficiency at about 50%. Hence, the present analysis provides a new theoretical guidance for designing dish collectors and operating the Stirling heat engine system.     

Optimal ratios of the piston speeds for a finite speed irreversible Carnot heat engine cycle

The performance of an irreversible Carnot heat engine cycle is analysed and optimized by using the theory of finite time thermodynamics based on Agrawal's [2009. A finite speed Curzon-Ahlborn engine. European Journal of Physics, 30 (3), 587–592] model of finite piston speed on the four branches and Petrescu et al.’s [2002b. Optimization of the irreversible Carnot cycle engine for maximum efficiency and maximum power through use of finite speed thermodynamic analysis. In: Proceedings of ECOS’2002, 3–5 July, Berlin, Germany, Vol. II, 1361–1368] model of a Carnot cycle engine with the finite rate of heat transfer, heat leakage from heat source to heat sink and irreversibilities caused by finite speed, friction and throttling through the valves. The finite piston speeds on the four branches are further assumed to be different, which is different from the model of constant speed of the piston on the four branches. Expressions of power output and thermal efficiency of the cycle are derived for a fixed cycle period and internal entropy generation rate. Numerical examples show that the curve of power output versus thermal efficiency is loop shaped, and there exist optimal finite piston speeds on the four branches which lead to the maximum power output and maximum thermal efficiency, respectively. The effects of the heat leakage coefficient and internal entropy generation rate on the optimal finite piston speed ratios are discussed.     

Stirling based fuel cell hybrid systems: An alternative for molten carbonate fuel cells

This paper presents a new design for high temperature fuel cell and bottoming thermal engine hybrid systems. Now, instead of the commonly used gas turbine engine, an externally fired - Stirling - piston engine is used, showing outstanding performance when compared to previous designs.Firstly, a comparison between three thermal cycles potentially usable for recovering waste heat from the cell is presented, concluding the interest of the Stirling engine against other solutions used in the past.Secondly, the interest shown in the previous section is confirmed when the complete hybrid system is analyzed. Advantages are not only related to pure thermal and electrochemical parameters like specific power or overall efficiency. Additionally, further benefits can be obtained from the atmospheric operation of the fuel cell and the possibility to disconnect the bottoming engine from the cell to operate the latter on stand alone mode. This analysis includes on design and off design operation.     

Thermodynamic analysis of a Stirling engine including regenerator dead volume

This paper provides a theoretical investigation on the thermodynamic analysis of a Stirling engine with linear and sinusoidal variations of the volume. The regenerator in a Stirling engine is an internal heat exchanger allowing to reach high efficiency. We used an isothermal model to analyse the net work and the heat stored in the regenerator during a complete cycle. We show that the engine efficiency with perfect regeneration doesn’t depend on the regenerator dead volume but this dead volume strongly amplifies the imperfect regeneration effect. An analytical expression to estimate the improvement due to the regenerator has been proposed including the combined effects of dead volume and imperfect regeneration. This could be used at the very preliminary stage of the engine design process.     

液压自由活塞发动机活塞运动规律动态仿真研究

为研究液压自由活塞发动机(HFPE)的活塞运动特性,建立了液压自由活塞发动机动态仿真模型,针对循环供油量、喷油定时、气门正时、压缩压力、负载压力等主要控制变量对活塞运动情况的影响进行了规律性研究.结果表明:各控制变量的变化影响活塞受力的变化,进而使活塞的下止点位置和压缩比发生变化,并影响发动机的正常运转和性能;循环油量与活塞膨胀行程长度、压缩能量与压缩比均近似呈线性关系;HFPE循环工作是一个多参数耦合和能量重新分配的复杂过程;执行器滞后引入的正时控制误差将是影响控制精度的重要因素.     

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%.