1.2 kW beta type Stirling engine with rhombic drive mechanism

Because of some advantages such as higher theoretical thermal efficiency, lower pollutant release, working with lower noisy, working with any kind of thermal energy, and having longer life time, Stirling engines receive attentions of academic workers. The development studies related to the drive mechanism as well as the other components of Stirling engine are progressing. In the present study, a beta type Stirling engine with a rhombic‐drive mechanism was manufactured and tested. Tests were performed at hot end temperatures of 600 and 800°C for five different stages of charge pressure ranging from 1 to 5 bar with 1 bar increments. Torque and power characteristics of the engine were deduced. The maximum engine torque and power were obtained as 18 Nm and 1215 W at engine speeds of 612 and 722 rpm, respectively, at 4 bar charging pressure. The cyclic work generations of the engine, which is an important parameter indicating the engine performance, were determined as 19, 27, and 25 J corresponding to 1, 3, and 5 bar charging pressures, respectively. In the experiments, the cylinder pressure variation was also measured at various charging pressures. While the charge pressure increases from 1 to 5 bar, the location of the maximum cylinder pressure ranged from 86° to 74° of crankshaft angle, which may have a bit influence on the engine performance. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

Development of a beta-type Stirling heat pump with rhombic drive mechanism by a modified non-ideal adiabatic model

In this paper, a thermodynamic model is developed for predicting the performance of a beta-type Stirling heat pump with rhombic drive mechanism for water heater and the model is validated by a 1-kW class prototype Stirling heat pump. In the present model, the working space is divided into expansion space, heat absorber, regenerator, heat rejecter and compression space. The pressure, mass and temperature variations of working fluid in each working space are predicted. The temperature variation of wall boundary is also taken into consideration. The temperature of working fluid in each working space and the temperature of wall boundary are obtained by solving energy equations simultaneously. Eventually, the pressure of working fluid in each working space can be corrected by using empirical formula of pressure drop. All the thermal properties of working fluid and wall boundary in each working space at each time step can be obtained by repeating the above process. Then, the performance of heat pump such as absorbing heat, rejecting heat, indicated power and COP can be calculated. A series of experimental measurements and comparisons are also conducted for validating present model. The results show that the prototype heat pump can produce 904 W heating power and 38°C hot water under 1 LPM water flow rate with 5 bar helium at 1000 rpm.     

Thermodynamic analysis of a gamma type Stirling engine in non-ideal adiabatic conditions

In this study, a thermodynamic analysis of a gamma type Stirling engine is performed by using a quasi steady flow model based on Urieli and Berchowitz's works. The Stirling engine analysis is performed for five principal fields: compression room, expansion room, cooler, heater and regenerator. The conservation law of the mass and the energy equations are derived for the related sections. A FORTRAN code is developed to solve the derived equations for all process parameters like pressure, temperature, mass flow, dissipation and convection losses for the different spaces (compression space, cooler, regenerator, heater and expansion space) as a function of the crank angle. The developed model gave more precise results for the pressure profile than the models available in the literature.     

Manufacturing and testing of a gamma type Stirling engine

In this study, a gamma type Stirling engine with 276 cc swept volume was designed and manufactured. The engine was tested with air and helium by using an electrical furnace as heat source. Working characteristics of the engine were obtained within the range of heat source temperature 700–1000 °C and range of charge pressure 1–4.5 bar. Maximum power output was obtained with helium at 1000 °C heat source temperature and 4 bar charge pressure as 128.3 W. The maximum torque was obtained as 2 N m at 1000 °C heat source temperature and 4 bar helium charge pressure. Results were found to be encouraging to initiate a Stirling engine project for 1 kW power output.     

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.     

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.     

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.     

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.     

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.     

Torque and power characteristics of a helium charged Stirling engine with a lever controlled displacer driving mechanism

This study presents test results of a Stirling engine with a lever controlled displacer driving mechanism. Tests were conducted with helium and the working fluid was charged into the engine block. The engine was loaded by means of a prony type micro dynamometer. The heat was supplied by a liquefied petroleum gas (LPG) burner. The engine started to run at 118 °C hot end temperature and the systematic tests of the engine were conducted at 180 °C, 220 °C and 260 °C hot end external surface temperatures. During the test, cold end temperature was kept at 27 °C by means of water circulation. Variation of the shaft torque and power with respect to the charge pressure and hot end temperature were examined. The maximum torque and power were measured as 3.99 Nm and 183 W at 4 bars charge pressure and 260 °C hot end temperature. Maximum power corresponded to 600 rpm speed.     

Numerical model for predicting thermodynamic cycle and thermal efficiency of a beta-type Stirling engine with rhombic-drive mechanism

This study is aimed at development of a numerical model for a beta-type Stirling engine with rhombic-drive mechanism. By taking into account the non-isothermal effects, the effectiveness of the regenerative channel, and the thermal resistance of the heating head, the energy equations for the control volumes in the expansion chamber, the compression chamber, and the regenerative channel can be derived and solved. Meanwhile, a fully developed flow velocity profile in the regenerative channel, in terms of the reciprocating velocity of the displacer and the instantaneous pressure difference between the expansion and the compression chambers, is derived for calculation of the mass flow rate through the regenerative channel. In this manner, the internal irreversibility caused by pressure difference in the two chambers and the viscous shear effects due to the motion of the reciprocating displacer on the fluid flow in the regenerative channel gap are included. Periodic variation of pressures, volumes, temperatures, masses, and heat transfers in the expansion and the compression chambers are predicted. A parametric study of the dependence of the power output and thermal efficiency on the geometrical and physical parameters, involving regenerative gap, distance between two gears, offset distance from the crank to the center of gear, and the heat source temperature, has been performed.     

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.     

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.     

Analytic model of solar power plant with a Stirling engine

An analytic model is proposed of a solar power plant (SPP) with a Stirling engine that is based on the isothermal model of the Stirling engine (SE) working process and is improved by account for the actual heat exchange, the hydraulic and mechanical losses in the SE, the losses in the electric generator, and also the basic parameters of the solar radiation concentrator.     

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.     

Exergy analysis of the woody biomass Stirling engine and PEM-FC combined system with exhaust heat reforming

The woody biomass Stirling engine (WB-SEG) is an external combustion engine that outputs high-temperature exhaust gases. It is necessary to improve the exergy efficiency of WB-SEG from the viewpoint of energy cascade utilization. So, a combined system that uses the exhaust heat of WB-SEG for the steam reforming of city gas and that supplies the produced reformed gas to a proton exchange membrane fuel cell (PEM-FC) is proposed. The energy flow and the exergy flow were analyzed for each WB-SEG, PEM-FC, and WB-SEG/PEM-FC combined system. Exhaust heat recovery to preheat fuel and combustion air was investigated in each system. As a result, (a) improvement of the heat exchange performance of the woody biomass combustion gas and engine is observed, (b) reduction in difference in the reaction temperature of each unit, and (c) removal of rapid temperature change of reformed gas are required in order to reduce exergy loss of the system. The exergy efficiency of the WB-SEG/PEM-FC combined system is superior to EM-FC.     

Design and manufacturing of a V-type Stirling engine with double heaters

Under the consideration of the solar energy potential of Turkey, a V-type Stirling engine having two heaters was designed, optimized and then manufactured. The prototype engine was tested in laboratory condition using an electrical heating system. Tests were conducted within the temperature range of 650–1000 °C with 50 °C increments. The pressure ranged from the ambient value to 2 bar with 0.5 bar increments at each stage of temperature. The maximum power was obtained at 950 °C and 1.0 bar charge pressure as 118 W.     

Dynamic simulation of a beta-type Stirling engine with cam-drive mechanism via the combination of the thermodynamic and dynamic models

Dynamic simulation of a beta-type Stirling engine with cam-drive mechanism used in concentrating solar power system has been performed. A dynamic model of the mechanism is developed and then incorporated with the thermodynamic model so as to predict the transient behavior of the engine in the hot-start period. In this study, the engine is started from an initial rotational speed. The torques exerted by the flywheel of the engine at any time instant can be calculated by the dynamic model as long as the gas pressures in the chambers, the mass inertia, the friction force, and the external load have been evaluated. The instantaneous rotation speed of the engine is then determined by integration of the equation of rotational motion with respect to time, which in return affects the instantaneous variations in pressure and other thermodynamic properties of the gas inside the chambers. Therefore, the transient variations in gas properties inside the engine chambers and the dynamic behavior of the engine mechanism should be handled simultaneously via the coupling of the thermodynamic and dynamic models. An extensive parametric study of the effects of different operating and geometrical parameters has been performed, and results regarding the effects of mass moment of inertia of the flywheel, initial rotational speed, initial charged pressure, heat source temperature, phase angle, gap size, displacer length, and piston stroke on the engine transient behavior are investigated.     

Exergetic analysis and performance evaluation of parabolic dish Stirling engine solar power plant

In this communication, a 50 MW_e design capacity parabolic dish Stirling engine solar power plant (PDSSPP) has been modeled for analysis, where 2000 units of parabolic dish Stirling engine each having capacity of 25 kW_e were considered to get desired capacity. An attempt has been made to carry out the energetic and exergetic analysis of different components of a solar power plant system using parabolic dish collector/receiver and Stirling engine. The energetic and exergetic losses as well as efficiencies for typical PDSSPP under the typical operating conditions have been evaluated. Variations of the efficiency of Stirling engine solar power plant at the part‐load condition are considered for year‐round performance evaluation. The developed model is examined at location Jodhpur (26.29°N, 73.03°E) in India. It is found that year‐round energetic efficiency varies from 15.57% to 27.09%, and exergetic efficiency varies from 16.83% to 29.18%. The unit cost of electric energy generation (kW_eh) is about 8.76 Indian rupees (INR), with 30 years life span of the plant and 10% interest rate on investment. Copyright © 2012 John Wiley & Sons, Ltd.