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.     

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.     

斯特林发动机的绝热分析

用绝热分析法建立并模拟了斯特林循环的理想绝热模型,仿真结果显示,增大循环压力能提高斯特林发动机的做功能力,这为以后建立非理想绝热模型和节点分析模型奠定了基础.     

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.     

Thermodynamic analysis of onset characteristics in a miniature thermoacoustic Stirling engine

This paper analyzes the onset characteristics of a miniature thermoacoustic Stirling heat engine using the ther-modynamic analysis method. The governing equations of components are reduced from the basic thermodynamic relations and the linear thermoacoustic theory. By solving the governing equation group numerically, the oscillation frequencies and onset temperatures are obtained. The dependences of the kinds of working gas, the length of resonator tube, the diameter of resonator tube, on the oscillation frequency are calculated. Meanwhile, the influences of hydraulic radius and mean pressure on the onset temperature for different working gas are also presented. The calculation results indicate that there exists an optimal dimensionless hydraulic radius to obtain the lowest onset temperature, whose value lies in the range of 0.30 0.35 for different working gases. Furthermore, the amplitude and phase relationship of pressures and volume flows are analyzed in the time-domain. Some experiments have been performed to validate the calculations. The calculation results agree well with the experimental values. Finally, an error analysis is made, giving the reasons that cause the errors of theoretical calculations.     

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.     

Investigation on power output of the gamma-configuration low temperature differential Stirling engines

This paper provides a study on power output determination of a gamma-configuration, low temperature differential Stirling engine. The former works on the calculation of Stirling engine power output are discussed. Results from this study indicate that the mean pressure power formula is most appropriate for the calculation of a gamma-configuration, low temperature differential Stirling engine power output.     

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.     

Integration of a free-piston Stirling engine and a moving grate incinerator

The feasibility of recovering the waste heat from a small-scale incinerator (designed by Industrial Technology Research Institute) and generating electric power by a linear free-piston Stirling engine is investigated in this study. A heat-transfer model is used to simulate the integration system of the Stirling engine and the incinerator. In this model, the external irreversibility is modeled by the finite temperature difference and by the actual heat transfer area, while the internal irreversibility is considered by an internal heat leakage. At a fixed source temperature and a fixed sink temperature, the optimal engine performance can be obtained by the method of Lagrange multipliers.From the energy and mass balances for the interesting incinerator with the feeding rate at 16 t/d, there is enough otherwise wasted energy for powering the Stirling engine and generate more than 50 kW of electricity.     

Optimization of the irreversible Stirling heat engine

The effects of inefficiencies in the compression, expansion and regeneration processes on engine performance have been evaluated theoretically for a Stirling heat engine operating in a closed regenerative thermodynamic cycle. The irreversible cycle has been optimized by using the maximum power density technique. Maximized power and maximized power density are obtained for different n_ex, τ, α_c, α_h, η_c, η_ex and η_reg values. The maximum efficiencies have been found very close to the values corresponding to the maximum power density conditions but far from the values at maximum power. It has been found that the engines designed by considering the maximum power density have high efficiencies and small sizes under the same prescribed conditions. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

Nodal analysis of a Stirling engine with concentric piston and displacer

To reduce the external volume of Stirling engines and to increase the specific power per unit volume, a novel mechanical arrangement is used where the power cylinder is concentrically situated inside the displacer cylinder. The inner heat transfer surface requirement and the thermodynamic performance characteristics are predicted preparing a nodal analysis in FORTRAN, where the inner volume of the engine is divided into 103 cells. Variation of the temperature in cells is calculated using the first law of thermodynamics, given for unsteady open systems, after arranging the enthalpy inflow and outflow terms. Volumes of cells are calculated using kinematic relations devised for the driving mechanism.The analysis indicates that the heats received from and delivered to the regenerator are not equal to each other. Therefore, the ends of the regenerator should be coupled with a heater and a cooler. The maximum thermal efficiency appears at the minimum mass of working fluid as the minimum thermal efficiency appears at the maximum mass of working fluid. The work increases up to a certain value of working fluid and then decreases. The thermal efficiency increases until a certain value of regenerator area and then decreases as well. Fluid temperature in the hot volume and cooler differs from the wall temperature at significant rates.     

Development of a compact simple unpressurized Watt-level low-temperature-differential Stirling engine

Despite the fast advance of modern technology, poverty is still a serious problem in many developing countries; and more than 1 billion people are having no access to electricity. For these people, even a few Watts of electricity supply for lighting can make a big difference. In this study, a simple, compact, unpressurized, Watt-level low-temperature-differential Stirling engine has been developed aiming to solve the lighting problem in developing countries. The engine in this study is compact. Yet, it is capable of delivering useful electrical power. It is a γ-type Stirling engine with twin power pistons. The diameter of the displacer cylinder is 220 mm, comparable to the size of a cooking pot, and the weight of the engine is under 5 kg. Two energy-conservation/heat-transfer enhancement measures have been incorporated into the engine's design: one is adopting a displacer/regenerator unit, and the other is machining engine-turn slotted grooves on its hot- and cold-end plates. CFD analysis showed that the combination of both measures could effectively improve the performance of the engine. Experiments were conducted to examine the engine's performance. In one experiment, the engine produced 3.7 W of electric power as temperature difference was 100°C, and its power was found to be almost linearly proportional to temperature difference. With a higher temperature difference of 140°C, the electric power reached 5.3 W. Another experiment that operated the engine for a prolonged period has proven the reliability of the engine's performance for long-time use. In practice, the engine can be operated by putting it on a stove table, and the residual heat from cooking is good enough to power the engine to produce usable electricity. Or it can be directly put on a wood fire to generate even higher electrical power.     

Empirical estimation of regenerator efficiency for a low temperature differential Stirling engine

An experimental method of regenerator evaluation is proposed in this paper. The configuration of the experimental equipment used in the method is similar to that of an alpha-configuration Stirling engine with a phase angle of 180°. The temperature of the hot side heat exchanger is controlled by an electric heater, and the heat sink was room air. An air conditioner controlled the temperature of the room air. The temperature and pressure of the working fluid were measured during the piston motion. A #18 stainless steel mesh was used as a regenerator matrix for a low temperature differential Stirling engine (LTDSE). The regenerator efficiency can be calculated based on the measurement results. The product of the swept volume, the density of the working fluid, the specific heat and the difference in the working fluid temperatures between the hot side and the cold side is greater than the amount of the internal energy fluctuation. The reason for this is assumed to be the temperature fluctuation in the region between the two heat exchangers. The walls of the region are made of acrylic resin. The amount of the temperature fluctuation in the region is assumed to be uniform. The regenerator efficiency is calculated as a function of the temperature fluctuation in the region. The evaluation method does not require a fast-response thermocouple. The prediction of the regenerator efficiency is possible basted on some experimental results of same matrix. Polyurethane foam and #18 stainless steel mesh, layered parallel to the stream line of the working fluid, were each tested. These materials can realize a non-rectangular regenerator without the generation of waste. Non-rectangular regenerator includes regenerator that can be installed into narrow gaps. The regenerator efficiency of the stainless steel mesh layered parallel to the stream line of the working fluid was significantly less in comparison to that of the normal mesh layers. In the polyurethane foam case, a pressure loss was observed.     

斯特林发动机管式加热器内振荡流动的换热特性实验研究

模拟管式加热器在斯特林发动机中的工作状态,研究加热器管内工作气体振荡流动的换热特性,得到气体压力、振荡频率等对换热的影响规律,进一步得到工作气体与管壁间的平均换热系数,并将结果转化为无量纲参数,比较稳定流动换热关联式计算结果与实验结果的偏差。实验结果可对斯特林发动机管式加热器设计、优化和换热性能预测提供参考。     

Experimental investigations of a gamma Stirling engine

The present work deals with the measurement and performance of a gamma Stirling engine of 500 W of mechanical shaft power and 600 rpm of maximal revolutions per minute. Series of measurements concerning the pressure distribution, temperature evolution, and brake power were performed. The study of the different functioning parameters such as initial charge pressure, engine velocity, cooling water flowrate, and temperature gradient (between the sources of heat) has been analyzed. The engine brake power increases with the initial charge pressure, with the cooling water flow, and with the engine revolutions per minute. The working fluid temperature measurements have been recorded in different locations symmetrically along both regenerator sides. The recorded temperature in regenerator side one is about 252 °C and about 174 °C in the opposite side (side two). It shows an asymmetric temperature distribution in the Stirling engine regenerator; consequently, heat transfer inside this porous medium is deteriorated. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance simulation of a low‐swirl burner for a Stirling engine

A new type of gas burner for Stirling engine that can recover adequate heat from exhaust gas was designed based on the plate heat exchanger and low‐swirl combustion technology, which consists of three components: a cyclone, a burner, and a circular plate heat exchanger. The circular plate heat exchanger tightly wound around the combustion chamber plays a high efficiency of heat recovery role. In consideration of the radial symmetry of the burner, a three‐dimensional numerical simulation was carried out by Ansys15. The velocity distribution, temperature distribution, and pressure distribution of the combustion gas were presented respectively. Strong backflow that came from the exhaust gas around the root of the flame in the combustion chamber and a vortex below the inlet of the exhaust gas channel were found, which were beneficial for the combustion and improving the uniformity of temperature distribution. Combustion behaviors of the burner under standard operating conditions were obtained, the highest temperature was about 2200 K in burner and the exhaust gas entered the plate heat exchanger at the temperature of 1375 K and exited at 464 K, with the waste heat recovery efficiency over 65.8%. And, the air‐fuel ratio and combustion power had negligible effect on the waste heat recovery efficiency.     

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.     

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.     

有限热源斯特林热机的优化性能研究

应用有限时间热力学方法,探索有限热源、热阻和回热损失的斯特林热机的优化性能,得到一些新的性能参数,所得结论可为斯特林热机的研制和优化设计提供些新理论指导。