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The paper presents a thermo-ecological analysis of a liquefied natural gas regasification system equipped with a Stirling engine. The proposed system includes an alpha configuration machine, working as a cold engine with the heat sink acting as the evaporator for the LNG and the upper heat source being at ambient temperature (sea water) or moderately higher. The engines are modelled using two approaches developed by the authors, that is a CFD model and a second-order one-dimensional model. First a small engine is modelled by both CFD and the second order approach to compare results and after confirming their similarity, due to a lower computational cost a larger machine is modelled with the second order model. Due to the heat transfer conditions being crucial for a Stirling cycle machine's performance, those are investigated. It is shown that the internal, convective heat transfer coefficients are much higher in cryogenic conditions than in typical ones. The results of engine assessment are used for the Thermo-ecological cost (TEC) analysis. Within the thermo-ecological analysis, the influence of selected parameters is demonstrated. Additionally the TEC of electricity generated in cold power plant is presented for different configurations. In the case of analysed Stirling systems savings of natural gas reach the level of only 0.5%. However, when TEC of electricity is calculated, the savings are at the level of 72%. The proposed theoretical investigations are the base for the acquisition of new knowledge in the field of possible ways of converting cryogenic exergy of LNG into electricity and optimization of this cycle with strong focus on ecological effects, including the TEC.

A modified theoretical model of dish solar Stirling engine was developed based on a Stirling cycle operating with finite shaft rotating speed and the energy balance equations at hot and cold ends. The convergence of solar receiver temperature and charged gas heat releasing temperature represent the stabilization of solar receiver and Stirling engine respectively, thus, to guarantee a steady operation of the overall system. Impacts of meteorological condition, operational parameter of Stirling engine on system performance were investigated and analyzed systematically. Results indicate that higher solar flux intensity improves system performance while wind deteriorates the system performance. With the input solar energy specified, optimal charged gas mass in Stirling engine exists corresponding to the maximal power output. More effective heater, regenerator and cooler contribute to better optimal system performance. Meanwhile, the charged gas mass optimized under the daily average solar flux intensity achieves the maximal mechanical work in a day with less computation. The maximal theoretical peak power output of 25 kW and overall efficiency of 44% are obtained as high performance heat exchangers are adopted and charged gas mass is optimized.

This paper designs and robustly schedules a novel AAHP (air to air heat pump) based ICHTF (industrial continuous heat treatment furnace) which is driven by a solar Stirling engine and a wind turbine. The proposed flame-making process equipped with two inside and outside air fans, an expansion valve, compressor, condenser, and an evaporator to supply the heating demand with the high-temperature more than 1000 K.The heating energy obtained from the AAHP is not produced during the combustion reactions but is transferred from the ambient air to the furnace chamber. Therefore, use of solar, wind and AAHP in an industrial furnace with no need to fossil fuels not only reduces the stack pollutant emissions and ozone-depleting substances, but also increases the economic savings in the consumptions of petroleum products and electricity, significantly. In this study, an energy-exergy based mathematical framework is comprehensively presented to model the proposed ICHTF in the presence of renewable energy sources such as air, solar, and wind. Moreover, an interval robust economic optimization strategy is introduced to minimize total energy procurement cost using the forecasted wind speed as inputs and taking into account the upper and lower limits of the wind power for modeling its uncertainties. In the robust model, the range of wind power is divided into several consecutive nested subintervals. The proposed ICHTF is simulated on a benchmark small-scale industrial sector which is located in a tropical region in order to minimize total electricity cost considering the operational constraints of Stirling cycle and AAHP considering the wind generation uncertainties. Simulation results reveal the feasibility and strength of the proposed ICHTF by solving a RNLP (robust nonlinear programming) problem using the CONOPT solver under GAMS (general algebraic mathematical system) environment.

Stirling engines can become a key component of distributed combined heat and power systems using renewable energy; however, their heat transfer surfaces suffer from overheating. To solve this, a low-temperature-difference indirect-heating kinematic Stirling engine employing a heat-transfer medium was developed. A new basic design method is devised by returning to the ideal Stirling cycle. The basic design of an engine optimized for temperature differences can be carried out using these criteria. To realize this basic design as an actual engine, an α+-type engine—the basic type suitable for low-temperature difference conditions—was developed. We developed a 10 kW-class engine using the basic design and type. Heat transfer oil was heated to 300 °C by burning wood biomass and circulated to the engine, which attained a maximum output of 14.3 kW, and a thermal efficiency of 15%. The engine was installed at the Minamisōma city community center and operates as a micro-combined heat and power system connected to the grid and independently during emergencies. The results show that the concept of the indirect heating low-temperature difference-type Stirling engine solves the main problem of its practical use, which can be used as a new distributed energy system.

The Stirling engine is a promising device to efficiently utilize external heat sources for various purposes. The understanding of the thermodynamic cycle of the gas parcels present in the Stirling engine is vital to its design and optimization. In this paper, a one-dimensional transient numerical model for Stirling engines is developed. A system for a β-type prototype was built and investigated by using both experimental and numerical methods. The relative error between the experimental and theoretical results measures

In this paper, a novel active solar heating system with self-blowing capability based on a quasi-Stirling cycle is modeled, developed, and primarily tested. First, the working principle of the proposed heating system is described and the possibility of power generation for air blowing based on the quasi-Stirling cycle is discussed. Then, a dynamic model for the proposed system is presented. Next, the presented mathematical model is used to simulate the system performance as well as to tune the control unit to acive the desired performance. Accordingly, the variations of gas pressure, temperature, and airflow rate over a working cycle are simulated through which the generated heat and power of the system can be evaluated. Finally, the experimental rig is developed and experimented. It is found that the proposed cogeneration system provides the ventilating air at a temperature of 333 K and an average airflow rate of 0.00994 m3/s besides the output work of 490 J in each working cycle practically. Moreover, the obtained experimental data from this first-stage developed technology reveal the feasibility of the presented idea, which can be further extended in the next stages of its development including design optimization, scalability, exergy analysis, and applicability in real fields.

An external heat source and a Stirling cycle are proposed for performance improvement of a direct carbon solid oxide fuel cell (DC-SOFC) system. The amount of the heat released in the DC-SOFC is determined based on a previously validated 2D tubular DC-SOFC model, in which the electrochemical reaction, chemical reactions, ion/electronic charge transport, mass transport and momentum transport are fully considered. Numerical calculations show that the overall heat released in the cell may be smaller than, equal to or larger than the heat required by the internal Boudouard reaction, and accordingly, three different operating modes of the system are given. The analytical expressions for the equivalent power output and efficiency for the DC-SOFC, Stirling cycle and the hybrid system are specified under different operating conditions. The results show that the power density and efficiency of the proposed system allow 4000 W m−2 and 30% larger than that of the stand-alone DC-SOFC at 30000 A m−2, respectively. Parametric studies also show that a higher operating temperature and a smaller distance between carbon layer and anode will increase the overall power density and efficiency of the proposed system.

In the paper, a second order thermodynamic analysis of a small scale alpha-type Stirling engine is presented. The developed mathematical model is based on the Finite Time Thermodynamics (FFT) approach and it is derived from the differential time dependent equations of energy and mass conservation. The engine model consists of three spaces: compression, expansion and regenerator. In contrast to available models, the model presented in this paper assumes polytropic processes in the compression and expansion spaces, which corresponds to the non-ideal heat transfer in these spaces. The results, obtained using the developed second order model, were compared with the results obtained using the Computational Fluid Dynamics (CFD) analysis of the same engine. A very good agreement between the second order model and the CFD model was achieved. Finally, the developed model was applied to analyse potential to recover cryogenic exergy of the Liquefied Natural Gas (LNG). The paper presents the results of the dimensional upscaling of the engine and the influence of the average working pressure. It was revealed that increasing the size of the engine or the average working pressure moves the engine to practically unachievable working conditions.

Recovering cold energy generated in the regasification process of liquefied natural gas (LNG) can help to improve the energy efficiency of LNG power generation systems, meanwhile, abundant low-grade waste heat can also be exploited from the exhaust gas of gas turbines. This study proposes to apply the thermoacoustic Stirling electric generator to recover LNG cold energy and waste heat simultaneously. A pair of linear alternators is directly coupled with the thermoacoustic loop by replacing the long and bulky resonator completely. Numerical simulation is conducted on the basis of the thermoacoustic theory to characterize and optimize the operations of the system. The effects of the back volumes of linear alternators, feedback tube length and regenerator length on the output performances are investigated. The distributions of key parameters, including pressure, volume flow rate, phase difference, acoustic power and exergy flow, are further studied. One design of the thermoacoustic Stirling electric generator operated with 4 MPa helium gas is capable of generating 2.3 kW electric power with the highest exergy efficiency of 0.253 when the cold and hot ends are maintained at 110 K and 500 K. Performances can be further improved if the conversion efficiency of the linear alternators is further increased.

LNG (liquefied natural gas) delivered by means of sea-ships is pressurized and then regasified before its introduction to the system of pipelines. The utilization of cryogenic exergy of LNG for electricity production without combustion of any its portion is analyzed. For the conversion of LNG cryogenic exergy into electricity, the Stirling engine is proposed to be applied. The theoretical thermodynamic model of Stirling engine has been applied. This model is used to investigate the influence of pinch temperature in heat exchangers, engine compression ratio and dead volumes ratios on the thermodynamic parameters of the Stirling engine. The results of simulation represent the input data for investigations of thermodynamic performance of the proposed system. In order to evaluate the thermodynamic performance of the proposed process, an exergy analysis has been applied. The exergy efficiency and influence of design and operational parameters on exergy losses are determined for each of the proposed system configurations. The obtained results represent the background for advanced exergy-based analyses, including thermo-ecological cost.

An unconventional Stirling engine is proposed and its theoretical analysis is performed. The engine belongs to a “cryogenic heat engine” that is fueled by cryogenic medium. Conventional “cryogenic heat engine” employs liquid air as a pressure source, but disregards its heat-absorbing ability. Therefore, its efficiency can only be improved by increasing vapor pressure, accordingly increasing the demand on pressure resistance and sealing. In the proposed engine, a closed cycle structure of Stirling engine is added to combine with the open cycle structure of a conventional cryogenic heat engine to achieve high efficiency and simplicity by utilizing the heat-absorbing ability of liquid air. Besides, the theoretical analysis of the proposed engine is performed. The Schmidt theory is modified to model temperature variation in the cold space of the engine, and irreversible characteristic of regenerator is incorporated in the thermodynamic model. The modeling results show that under the same working pressure, the efficiency of the proposed engine is potentially higher than that of conventional ones and to achieve the same efficiency, the working pressure could be lower with the new mechanism. Composition of exergy loss in the proposed engine is analyzed.

The assumptions of second order Stirling engine models were reviewed. An ideal adiabatic plus simple heat exchanger model was developed. The model included the external components such as the fan, combustor, and preheater. The external heat transfer to the engine heater was modeled using a log-mean-temperature difference for a constant tube surface temperature. The performance of the model of the external components compared reasonably well to experimental data. The performance of the complete engine model was also compared to experimental data of the GPU-3. By adjusting the flow dissipation to better account for unsteady flow conditions and compressibility effects, the complete engine model was able to predict engine power and brake specific fuel consumption to within ±14% over a wide range of engine speeds and mean pressures. This analysis and others suggest that second order models of Stirling engines need to account for the gradient of the divergence of velocity term in the compressible momentum equation if the mean engine pressure is low enough (less than 3.0 MPa) and the engine speed is high enough (above 30 Hz).

In this paper, an irreversible thermodynamic cycle working between two constant temperature external reservoirs is proposed to model the practical Stirling engine by applying finite time thermodynamics (FTT). To analyze the regenerative processes, the regenerator is assumed to consist of numerous smaller heat reservoirs with individual temperature, and the irreversible heat transfer occurs between the working fluid and these smaller heat reservoirs. To analyze the expansive and compressive processes, polytropic processes are adopted to model the expansive and compressive processes, and corresponding polytropic exponents are obtained by thermodynamics for the first time. Based on the proposed thermodynamic model, the expression of thermal efficiency and output power are derived. In addition, the effects of thermodynamic parameters on power and efficiency are investigated to evaluate the performance of the proposed model. To optimize the proposed Stirling cycle model, an intelligent optimization algorithm named multi-objective particle swarm optimization based on crowding distance (MOPSOCD) is adopted to optimize the output power and thermal efficiency simultaneously.

Cryogenic generation is one of the most important ways to utilize cold energy during LNG (liquefied natural gas) regasification. This paper fundamentally investigates LNG cryogenic generation with the Stirling cycle method based on previous studies. A basic process of LNG cryogenic generation with the Stirling cycle was presented initially with seawater and LNG as heat source and heat sink. And its thermodynamic analysis was performed to verify the theoretical feasibility of the Stirling cycle method. The generating capacity, the exergy efficiency and the cold energy utilization efficiency of the basic process were also calculated. Subsequently, the influences of evaporation pressure on net work, equipment performance and comprehensive efficiency of cold energy utilization were discussed and the effect of LNG mass flow as well as the ambient temperature was also studied. Finally an improved process of LNG cryogenic generation with Stirling cycle method combined with an air liquefaction process is proposed as feasibility in improvements of the basic process.

This work explores the scaling effects for FPSE (free piston Stirling engines), which are known for their simple architecture and potentially high thermodynamic performances. Scaling laws are given and their potential for miniaturization is highlighted. A simple model which allows the design of the geometrical parameters of the heat exchangers, the regenerator and the masses of the pistons is proposed. It is based on the definition of six characteristic dimensionless groups. They are derived from the physics underlying the behavior of the free piston Stirling machine and their relevancy is backed up by comparisons between documented Stirling engines from the literature. Keeping constant values for each group throughout the scaling range theoretically ensures constant performance. The main losses of Stirling engine (heat conduction loss, reheat loss in the regenerator, pressure drop and gas-spring hysteresis) can be expressed as a function of the geometrical and operating parameters. Additionally, the consequences of leakage due to the manufacturing precision of pistons architectures are underlined. From the proposed scaling laws, potential power and efficiency of Stirling cycle engines at a millimeter scale can be anticipated. It appears that the power density increases with miniaturization. It is also shown that the dynamic masses related to the engine size are increased when scaling down and that the gap leakage presents the highest detrimental effects on the efficiency. These results call for dedicated architectures for micro-engines.

A theoretical model for predicting thermodynamic behavior of thermal-lag Stirling engine is presented in this study. Without a displacer and its link, the thermal-lag engine contains only a moving part (piston) and a static part (regenerative heater) in engine's cylinder and hence, is regarded as a unique type of Stirling engines that featuring rather simple mechanical structure. In this study, a numerical simulation of thermodynamic behavior of the thermal-lag Stirling engine is performed based on the theoretical model developed. Transient variations of temperatures, pressures, pressure difference, and working fluid masses in the individual working spaces of the engine are predicted. Dependence of indicated power and thermal efficiency on engine speed has been investigated. Then, optimal engine speeds at which the engine may reach its maximum power output and/or maximum thermal efficiency is determined. Furthermore, effects of geometrical and operating parameters, such as heating and cooling temperatures, volumes of the chambers, thermal resistances, stroke of piston, and bore size on indicated power output and thermal efficiency are also evaluated.

In order to investigate the Stirling engine implementation technology, a Solo Stirling Engine V161 cogeneration module has been installed at the Laboratory of Applied Thermodynamics of National Technical University of Athens. A special thermodynamic analysis of the engine's performance has been conducted introducing and utilizing specially designed computing codes along with the thermal balance study of the unit. Measurements were conducted under different operational conditions concerning various heat load stages of the engine, working pressure, as well as electric power production. Analysis of the experimental results has shown that the overall performance of the Stirling unit proved very promising and quite adequate for various areal applications, equally competing with other CHP systems. The performance of the unit experienced significant stability all over the operating range. The power stand ratio 0.35 differentiates Stirling cogeneration units from others that use diverging technologies significantly. The energy savings using a Stirling CHP unit, in respect to the concurrent use of a thermal and an electrical system at the same equivalent power has revealed 36.8%.

The aim of this study was to investigate the feasibility of utilising a Stirling cycle engine as an exhaust gas waste heat recovery device for an Otto cycle internal combustion engine (ICE) in the context of an automotive power plant. The hybrid arrangement would produce increased brake power output for a given fuel consumption rate when compared to an ICE alone. The study was dealt with from an energy system perspective with design practicalities such as power train integration, location of auxiliaries, manufacture costs and other general plant design considerations neglected. The study necessitated work in two distinct areas: experimental assessment of the performance characteristics of an existing automotive Otto cycle ICE and mathematical modelling of the Stirling cycle engine based on the output parameters of the ICE. It was subsequently found to be feasible in principle to generate approximately further 30% useful power in addition to that created by the ICE by using a Stirling cycle engine to capture waste heat expelled from the ICE exhaust gases over the complete range of engine operating speeds.

The objective of this study has been to create a Stirling engine model for studying the effects of regenerator matrix temperature oscillations on Stirling engine performance. A one-dimensional model with axial discretisation of engine components has been formulated using the control volume method. The model contains a system of ordinary differential equations (ODEs) derived from mass and energy balances for gas filled control volumes and energy balances for regenerator matrix control masses. Interpolation methods with filtering properties are used for state variables at control volume interfaces to reduce numerical diffusion and/or non-physical oscillations. Loss mechanisms are included directly in the governing equations as terms in the mass and energy balances. Steady state periodic solutions that satisfy cyclic boundary conditions and integral conditions are calculated using a custom built shooting method. It has been found possible to accurately solve the stiff ODE system that describes the coupled thermodynamics of the gas and the regenerator matrix and to reliably find periodic steady state solutions to the model. Preliminary results indicate that the regenerator matrix temperature oscillations do have significant impact on the regenerator loss, the cycle power output, and the cycle efficiency and thus deserve further study.

This communication presents an investigation of a finite time thermodynamic analysis of an endoreversible Stirling heat engine. Finite time thermodynamics has been applied to maximize the power output and the corresponding thermal efficiency of an endoreversible Stirling heat engine with internal heat loss in the regenerator and for the finite heat capacity of the external reservoirs. The effect of the effectiveness of the various heat exchangers, the inlet temperatures of external heat reservoirs on the power output and the corresponding thermal efficiency have been studied. It is seen that an endoreversible Stirling heat engine with an ideal regenerator ( ϵ R =1.00) is as efficient as an endoreversible Carnot heat engine. It is also found that the maximum power output increases with the heat capacitance rates and effectiveness of the source/sink side heat exchangers while thermal efficiency increases with the effectiveness of the regenerator.

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.

The power output and thermal efficiency of a finite-time, optimized, extra-terrestrial, solar-radiant Stirling heat engine have been studied. The thermodynamic model adopted is a regenerative gas Stirling cycle coupled to a heat source and heat sink by radiant heat transfer. Both the heat source and sink are assumed to have infinite heat-capacity rates. Expressions are obtained for optimum power and efficiency at optimum power for a cycle based on higher and lower temperature bounds.

We present a finite-time thermodynamic analysis of the Stirling engine cycle based on mass and energy balances with associated heat-transfer-rate equations. These governing equations are formulated as normalized ordinary differential equations which are solved numerically. The effects of heat-transfer contact time and regeneration on power output and efficiency are studied. The results show that there exists an optimum power output for a given engine design, based on engine speed and heat-transfer contact time.

An optimal power analysis is conducted on an endoreversible Stirling cycle with perfect regeneration. The endoreversible cycle is one in which the external heat transfer processes are the only irreversible processes of the cycle. Maximum power and efficiency at maximum power are obtained for the cycle based upon higher and lower temperature bounds. These results provide additional criteria for use in the study and performance evaluation of Stirling engines.