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.     

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。     

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...     

Thermodynamic optimization of Stirling heat engine with methane gas using finite speed thermodynamic model

With the daily rise in environmental issues due to the use of conventional fuels, researchers are motivated to use renewable energy sources. One of such waste heat and low-temperature differential driven energy sources is the Stirling engine. The performance of the Stirling engine can be improved by finding out the optimum operating and geometrical parameters with suitable working gas and thermal model. Based on this motivation, the current work focuses on the multiobjective optimization of the Stirling engine using the finite speed thermodynamic model and methane gas as the working fluid. Considering output power and pressure drop as two objective functions, the system is optimized using 11 geometrical and thermal design parameters. The optimization results are obtained in the form of the Pareto frontier. A sensitivity assessment is carried out to observe the decision variables, which are having a more sensitive effect on the optimization objectives. Optimization results reveal that 99.83% change in power output and 78% change in total pressure drop can take place in the two-dimensional optimization space. The optimal solution closest to the ideal solution has output power and pressure drop values as 12.31 kW and 22.76 kPa, respectively.     

Multi-objective optimization for GPU3 Stirling engine by combining multi-objective algorithms

Stirling engine has become preferable for high attention towards the use of alternate renewable energy resources like biomass and solar energy. Stirling engine is the main component of dish Stirling system in thermal power generation sector. Stirling engine is an externally heating engine, which theoretical efficiency is as high as Carnot cycle's, but actual ones are always far below compared with the Carnot efficiency. A number of studies have been done on multi-objective optimization to improve the design of Stirling engine. In the current study, a multi-objective optimization method, which is a combination of multiple optimization algorithms including differential evolution, genetic algorithm and adaptive simulated annealing, was proposed. This method is an attempt to generalize and improve the robustness and diversity with above three kinds of population based meta-heuristic optimization techniques. The analogous interpreter was linked and interchanged to find the best global optimal solution for Stirling engine performance optimization. It decreases the chance of convergence at a local minimum by powering from the fact that these three algorithms run parallel and members from each population and technique are swapped. The optimization considers five decision variables, including engine frequency, mean effective pressure, temperature of heating source, number of wires in regenerator matrix, and the wire diameter of regenerator, as multiple objectives. The Pareto optimal frontier was obtained and a final optimal solution was also selected by using various multi-criteria decision making methods including techniques for Order of Preference by Similarity to Ideal Solution and Simple Additive Weighting. The multi-objective optimization indicated a way for GPU-3 Stirling engine to obtain an output power of more than 3 kW and an increase by 5% in thermal efficiency with significant decrease in power loss due to flow resistance.     

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.     

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.     

分置式斯特林发动机热力性能的仿真

对斯特林发动机的压缩与膨胀过程进行了变质量系统热力学分析。利用等温模型分析法,引入流动阻力损失的计算模型,模拟了分置式斯特林发动机内部工质的压力等参数的动态变化规律。仿真结果表明：斯特林发动机在运行过程中压缩腔与膨胀腔的气体压力并不时时相等;提高发动机的转速和高温热源温度,可以增加发动机的输出功率。     

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.     

Design and performance optimization of GPU-3 Stirling engines

To increase the performance of Stirling engines and analyze their operations, a second-order Stirling model, which includes thermal losses, has been developed and used to optimize the performance and design parameters of the engine. This model has been tested using the experimental data obtained from the General Motor GPU-3 Stirling engine prototype. The model has also been used to investigate the effect of the geometrical and physical parameters on Stirling engine performance and to determine the optimal parameters for acceptable operational gas pressure. When the optimal design parameters are introduced in the model, the engine efficiency increases from 39% to 51%; the engine power is enhanced by approximately 20%, whereas the engine average pressure increases slightly.     

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.     

小型斯特林发电测试系统的设计

阐述了小型斯特林发电测试系统的组成部分,并对发动机的热腔温度、冷腔温度、转速、输出扭矩、发电机输出电压、电流等重要参数进行测量,并对结果进行了分析和讨论。     

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.     

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.     

Introducing an integrated SOFC,linear Fresnel solar field,Stirling engine and steam turbine combined cooling,heating and power process

A new integrated combined cooling, heating and power system which includes a solid oxide fuel cell, Stirling engine, steam turbine, linear Fresnel solar field and double effect absorption chiller is introduced and investigated from energy, exergy and thermodynamic viewpoints. In this process, produced electrical power by the fuel cell and steam turbines is 6971.8 kW. Stirling engine uses fuel cell waste heat and produces 656 kW power. In addition, absorption chiller is driven by waste heat of the Stirling engine and generates 2118.8 kW of cooling load. Linear Fresnel solar field produces 961.7 kW of thermal power as a heat exchanger. The results indicate that, electrical, energy and exergy efficiencies and total exergy destruction of the proposed system are 49.7%, 67.5%, 55.6% and 12560 kW, respectively. Finally, sensitivity analysis to investigate effect of the different parameters such as flow rate of inputs, outlet pressure of the components and temperature changes of the solar system on the hybrid system performance is also done.     

A four power-piston low-temperature differential Stirling engine using simulated solar energy as a heat source

In this paper, the performances of a four power-piston, gamma-configuration, low-temperature differential Stirling engine are presented. The engine is tested with air at atmospheric pressure by using a solar simulator with four different solar intensities as a heat source. Variations in 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 actual energy input of 1378 W and a heater temperature of 439 K, the engine approximately produces a maximum torque of 2.91 N m, a maximum shaft power of 6.1 W, and a maximum brake thermal efficiency of 0.44% at 20 rpm.     

内燃机有限时间内不可逆循环热力学分析

本文讨论了内燃机循环在逐步考虑各种主要不可逆因素后所构成的一系列新的热力学模型下有限时间热力学分析，重点寻找出在规定的模型下其循环最大输出功率与对应的热效率之间的关系，给出了有限时间热力学意义下内燃机循环新的性能界限，它们对实际内燃机性能的评估及改进有一定的指导意义。     

Optimum absorber temperature of a once-reflecting full conical concentrator of a low temperature differential Stirling engine

This paper provides a theoretical investigation on the optimum absorber temperature of a once-reflecting full conical concentrator for maximizing overall efficiency of a solar-powered low temperature differential Stirling engine. A mathematical model for the overall efficiency of the solar-powered Stirling engine is developed. The optimum absorber temperature for maximum overall efficiency for both limiting conditions of maximum possible engine efficiency and maximum possible engine power output is determined. The results indicated that the optimum absorber temperatures calculated from these two limiting cases are not significantly different. For a given concentrated solar intensity, the maximum overall efficiency characterized by the condition of maximum possible engine power output is very close to that of the real engine of 55% Carnot efficiency, approximately.     

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.     

Analytical model for predicting the effect of operating speed on shaft power output of Stirling engines

This paper is concerned with numerical predictions of relationship between operating speed and shaft power output of Stirling engines. Temperature variations in expansion and compression spaces as well as the shaft power output corresponding to different operating speeds were investigated by using a lumped-mass transient model. Effects of major operating parameters on power output were studied. Results show that as the operating speed increased, temperature difference between the expansion and compression spaces was reduced and as a result, the shaft work output decreased. However, the shaft power output is determined in terms of the shaft work output and the operating speed. When the operating speed was elevated, the shaft power output reached a maximum at a critical operating speed. Over the critical operating speed, the shaft power output decreased in high-speed regime. In addition, as air mass was reduced, either a decrease in thermal resistances or an increase in effectivenesses of the regenerator leads to an increase in the engine power.