Optimal regenerator performance in Stirling engines

The key component of a Stirling engine is its regenerative heat exchanger. This device is subject to losses due to dissipation arising from the flow through the regenerator as well as due to imperfect heat transfer between the regenerator material and the gas. The magnitudes of these losses are characterized by the Stanton number St and the Fanning friction factor f, respectively. Using available data for the ratio St/f, results are found for the Carnot efficiency and the power output of the regenerator. They depend on the conductance and on the ratio of pressures at the two sides of the regenerator. Optimum results for efficiency and power output of the regenerator are derived in the limit of zero Mach number. The results are applied to the Stirling engine. The efficiency and the power output of the engine are found for given amplitude of the compression piston. Optimization with respect to regenerator conductance and piston phase angle leads to a maximum possible value of the power output. Under optimal conditions, the Carnot efficiency just below this maximum is close to 100%. Copyright © 2009 John Wiley & Sons, Ltd.     

Thermodynamic multi-objective optimization of a solar-dish Brayton system based on maximum power output,thermal efficiency and ecological performance

Solar-dish Brayton system driven by the hybrid of fossil fuel and solar energy is characterized by continuously stable operation, simplified hybridization, low system costs and high thermal efficiency. In order to enable the system to operate with its highest capabilities, a thermodynamic multi-objective optimization was performed in this study based on maximum power output, thermal efficiency and ecological performance. A thermodynamic model was developed to obtain the dimensionless power output, thermal efficiency and ecological performance, in which the imperfect performance of parabolic dish solar collector, the external irreversibility of Brayton heat engine and the conductive thermal bridging loss were considered. The combination of NSGA-II algorithm and decision makings was used to realize multi-objective optimization, where the temperatures of absorber, cooling water and working fluid, the effectiveness of hot-side heat exchanger, cold-side heat exchanger and regenerator were considered as optimization variables. Using the decision makings of Shannon Entropy, LINMAP and TOPSIS, the final optimal solutions were chosen from the Pareto frontier obtained by NSGA-II. By comparing the deviation index of each final optimal solution from the ideal solution, it is shown that the multi-objective optimization can lead to a more desirable design compared to the single-objective optimizations, and the final optimal solution selected by TOPSIS decision making presents superior performance. Moreover, the fitted curve between the optimal power output, thermal efficiency and ecological performance derived from Pareto frontier is obtained for better insight into the optimal design of the system. The sensitivity analysis shows that the optimal system performance is strongly dependent on the temperatures of absorber, cooling water and working fluid, and the effectiveness of regenerator. The results of this work offer benefits for related theoretic research and basis for solar energy industry.     

斯特林发动机瞬态模型及特性分析

为获得斯特林发动机的动态特性和优化方案,将损失机制和压力梯度耦合进控制方程中,提出一维瞬态斯特林循环分析模型及分析方法,并针对GPU-3斯特林发动机进行模型验证和特性分析.模型的指示功率相对误差平均值约为4.8％,热效率的相对误差小于1％.当氦气工质在热源温度为977 K、平均压强为2.76 MPa时,输出功率随转速的...     

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.     

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.     

Maximum power-conversion efficiency for the utilization of solar energy

The overall efficiency of solar thermal power plants is investigated for estimating the upper limit of their practical performances. This study consists of the theoretical optimization of the heat engine and the optimization of the overall system efficiency, which is the product of the efficiency of the solar collector and the efficiency of the heat engine. In order to obtain a more realistic performance of the solar thermal power plant, the solar collector concentration ratio, the diffused solar radiation and the convective and radiative heat losses of the solar collector are taken into account. Instead of the classical Carnot efficiency, the efficiency at maximum power is used as the optimal conversion efficiency of a heat engine. By means of simple calculations, the optimal overall system efficiency and the corresponding operating conditions of the solar collector are obtained. The results of the present work provide an accurate guide to the performance estimation and the design of solar thermal power plants.     

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.     

Multi-objective optimization in a finite time thermodynamic method for dish-Stirling by branch and bound method and MOPSO algorithm

There are various analyses for a solar system with the dish-Stirling technology. One of those analyses is the finite time thermodynamic analysis by which the total power of the system can be obtained by calculating the process time. In this study, the convection and radiation heat transfer losses from collector surface, the conduction heat transfer between hot and cold cylinders, and cold side heat exchanger have been considered. During this investigation, four objective functions have been optimized simultaneously, including power, efficiency, entropy, and economic factors. In addition to the four-objective optimization, three-objective, two-objective, and single-objective optimizations have been done on the dish-Stirling model. The algorithm of multi-objective particle swarm optimization (MOPSO) with post-expression of preferences is used for multi-objective optimizations while the branch and bound algorithm with pre-expression of preferences is used for single-objective and multi-objective optimizations. In the case of multi-objective optimizations with post-expression of preferences, Pareto optimal front are obtained, afterward by implementing the fuzzy, LINMAP, and TOPSIS decision making algorithms, the single optimum results can be achieved. The comparison of the results shows the benefits of MOPSO in optimizing dish Stirling finite time thermodynamic equations.     

Finite time thermodynamic evaluation of endoreversible Stirling heat engine at maximum power conditions

Maximum power and efficiency at the maximum power point of an endoreversible Stirling heat engine with finite heat capacitance rate of external fluids in the heat source/sink reservoirs with regenerative losses are treated. It was found that the thermal efficiency depends on the regenerator effectiveness and the internal irreversibility resulting from the working fluid for a given value of reservoir temperature. It was also concluded that it is desirable to have larger heat capacity of the heat sink in comparison to the heat source reservoir for higher maximum power output and lower heat input.     

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.     

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.     

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.     

Design and optimization of a non-TEMA type tubular recuperative heat exchanger used in a regenerative gas turbine cycle

A special non-TEMA type tubular recuperative heat exchanger used as a regenerator of a gas turbine cycle is considered for multi-criteria optimization. It is assumed that the recuperator is designed for an existing gas turbine cycle to be retrofitted. Three scenarios for optimization of the proposed system have been considered. In one scenario, the objective is minimizing the cost of recuperator; while in another scenario maximizing the cycle exergetic efficiency is considered. In third scenario, both objectives are optimized simultaneously in a multi-objective optimization approach. Geometric specification of the recuperator including tubes length, tubes outside/inside diameters, tube pitch in the tube bundle, inside shell diameter, outer and inner tube limits of the tube bundle and the total number of disc and doughnut baffles are considered as decision variables. Combination of these objectives and decision variables with suitable engineering and physical constraints (including NO_x and CO emission limitations) makes a set of MINLP optimization problem. Optimization programming in MATLAB is performed using one of the most powerful and robust multi-objective optimization algorithms namely NSGA-II. This approach which is based on the Genetic Algorithm is applied to find a set of Pareto optimal solutions. Pareto optimal frontier is obtained and a final optimal solution is selected in a decision-making process. It is shown that the multi-objective optimization scenario can be considered as a generalized optimization approach in which balances between economical viewpoints of both heat exchanger manufacturer and end user of recuperator.     

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。     

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.     

广义不可逆卡诺热机的生态学最优性能

以反映热机功率与熵产率之间最佳折衷的“生态学”准则为目标，综合考虑热阻、热漏及其它不可逆性对卡诺热机性能的影响，导出牛顿传热规律下循环的生态学最优性能，由数值计算分析比较了热漏、内不可逆性的影响特点。生态学优化以牺牲小部分输出功率为代价，较大地降低了循环的熵产率，而且在一定程度上提高了热机效率。因此，生态学目标函数不仅反映了输出功率和熵产率之间的最佳折衷，而且反映了输出功率和热效率之间的最佳折衷。     

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...     

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.     

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。     

α-Stirling hydrogen engines for concentrated solar power

α-Stirling engines are receiving more and more attention for applications of concentrated solar power in small power installations (15–30 kW). The design of these engines has not experienced in recent years the breakthrough needed to deliver close to the Carnot Cycle energy conversion efficiencies. The delivered efficiencies are limited to mid-to-high 20% in the typical installations “Dish Stirling”. Here we review the latest studies made on α-Stirling engines, unfortunately mostly based on theoretical models of limited reliability, but also including very few examples of Computer-Aided Engineering (CAE) modeling followed by prototyping and testing. Finally, we present in detail one CAE model of an α-Stirling engine delivering energy conversion efficiencies of 42% with hydrogen as working fluid and adopting one hot cylinder, one cold cylinder, and one regenerator, with the hot fluid temperature of 800 °C. This efficiency is much higher than current air microturbines, which may deliver efficiencies of only about 20% working at much lower temperatures.