The effect of displacer material on the performance of a low temperature differential Stirling engine

In this study, a gamma‐type low temperature differential Stirling engine was designed and manufactured. The displacer and piston of the engine were concentrically situated to each other. The engine was tested by using a liquefied petroleum gas burner at laboratory conditions. The working fluid was ambient air at atmospheric pressure. Test procedure intended to investigate the speed‐torque and speed‐power characteristics of the engine depending on the hot‐end temperature. Two different displacers made of aluminum alloy and medium density fiberboard were used. The maximum torque and power obtained were 0.166 Nm at 125 rpm speed and 3.06 W at 215 rpm speed, respectively, at 160 °C hot‐end temperature with medium density fiberboard displacer. Copyright © 2011 John Wiley & Sons, Ltd.     

Design consideration of low temperature differential double-acting Stirling engine for solar application

This paper presents design considerations to be taken in designing of a low temperature differential double-acting Stirling engine for solar application. The target power source will be a thermosiphon solar water heater with integrated storage system, which will supply a constant source temperature of 70 °C. Hence, the system design is based on a temperature difference of 50 °C, assuming that the sink is kept at 20 °C. During the preliminary design stage, the critical parameters of the engine design are determined according to the Schmidt analysis, while the third order analysis was used during the design optimisation stage in order to establish a complete analytical model for the engine. The heat exchangers are designed to be of high effectiveness and low pressure-drop, and are made from a 0.015 m tube, while the porosity of the steel wool of 0.722 is used for the regenerator matrix. Upon optimisation, the optimal engine speed is 120 rpm with the swept volume of 2.3 l, and thus the critical engine parameters are found to be the bore diameter of 0.20 m. In addition, the volumes of heater, cooler and regenerator are 1.3 l, 1.3 l and 2.0 l volumes, respectively.     

Numerical prediction of performance of a low-temperature-differential gamma-type Stirling engine

Abstract

In this study, a numerical simulation model is used to analyze thermodynamic performance of a low temperature-differential gamma-type Stirling engine by adjusting some values of the operating and geometrical parameters around a designated baseline case. The influences of these operating and geometrical parameters on engine performance such as working fluid materials, the stroke of piston and displacer, charged pressure, the heating temperature, and so on, are concerned. A numerical simulation model is established based on turbulent flow assumption and the realizable k – ε model is employed to solve the flow and thermal fields in the engine. In regard to flow in regenerator, Darcy–Forchheimer model was used to depict dynamic behavior of working fluid. Besides, thermal equilibrium model was used for solving the energy equation. Finally, working fluid in the engine undergoes a wide range of pressure and temperature so the effects of temperature and pressure on the viscosity and thermal conductivity of the working fluid are required to include. Thermal conductivity of porous medium matrix is affected by wide range of temperature as well.     

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.     

Improved Stirling engine performance through displacer surface treatment

This study intended to improve the performance of the beta‐type Stirling engine, being developed by the authors for solar energy and low‐grade heat sources, by means of displacer surface treatments. Three different displacers were manufactured and tested where one of them was without any surface treatment, other was zirconium coated with 0.15 mm thickness, and the other was helically knurled with 0.30 mm track depth. Because of good thermo‐physical properties, helium was used as the working fluid. The heat was supplied by an LPG burner. Tests were conducted at 360±10°C hot end temperature. The highest engine power was obtained with knurled displacer as 250 W at 545 rpm speed and corresponding to this power 4.38 Nm torque was obtained. This was followed by coated and smooth displacers. Power increments provided by the knurled displacer are 40 and 60% compared with the zirconium‐coated and untreated displacers. Increments of knurled displacer's torque compared with that of coated and untreated displacers are 13 and 30%, respectively. Copyright © 2009 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.     

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.     

A comprehensive review on modeling and performance optimization of Stirling engine

Modeling with optimization has become a ubiquitous practice in the field of Stirling engine. A plethora of studies in the literature is dedicated in developing a feasible optimized model that can precisely predict the performance of Stirling engine. Hence, the purpose of this article is to compile and expansively review the thermodynamic models and optimization efforts made in pursuit of performance enhancement of the Stirling engine. An extensive range of models available in the literature is painstakingly discussed. Likewise, a wide variety of available optimization techniques spanning from conventional experimental and univariate methods to more complex multiobjective optimization approach are critically reviewed. A comparative analysis of the models is carried out based on the accuracy of their predictability of the performance of Stirling engines. Results obtained from the models are validated through the experimental data of the GPU-3 Stirling engine prototype. Several optimization techniques are investigated based on the effective and efficient optimization of operating and geometric parameters of the Stirling engine. The review concluded that the Comprehensive Polytropic Model of Stirling engine (CPMS) demonstrated better accuracy in comparison with other models. In addition, the multiobjective particle swarm optimization (MOPSO) technique was found to be effective and computationally efficient.     

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.     

Optimization of Stirling engine performance based on an experimental design approach

The Stirling engine performances depend on several physicals characteristics and functioning parameters. The influence of each parameter and of their interactions is difficult to achieve with classical univariate studies. The experimental design is an alternative to identify the parameters sets allowing optimal Stirling engine performances. Hence, a four factor Central Composite Rotatable Design was used to observe the effect of cooling water flowrate, initial charge pressure, heating temperature, and operation time on a Stirling engine brake power. The influence of each parameter and the effect of the interaction between two or three parameters on the engine performances are presented and discussed. Using the surface response method, it appears that initial charge pressure and heating temperature are the more influencing parameters on the Stirling engine performances. With modeling, optimal conditions for the Stirling engine functioning are the following: charge pressure of 8 bar, heating temperature of 500 °C, and cooling water flow rates of 7.34 l/min, independent of the engine operation time. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis and design consideration of mean temperature differential Stirling engine for solar application

This article presents a technical innovation, study of solar power system based on the Stirling dish (SD) technology and design considerations to be taken in designing of a mean temperature differential Stirling engine for solar application. The target power source will be solar dish/Stirling with average concentration ratio, which will supply a constant source temperature of 320 °C. Hence, the system design is based on a temperature difference of 300 °C, assuming that the sink is kept at 20 °C. During the preliminary design stage, the critical parameters of the engine design are determined according to the dynamic model with losses energy and pressure drop in heat exchangers was used during the design optimisation stage in order to establish a complete analytical model for the engine. The heat exchangers are designed to be of high effectiveness and low pressure-drop. Upon optimisation, for given value of difference temperature, operating frequency and dead volume there is a definite optimal value of swept volume at which the power is a maximum. The optimal swept volume of 75 cm³ for operating frequency 75 Hz with the power is 250 W and the dead volume is of 370 cm³.     

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.     

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.     

Optimization of a dual free piston Stirling engine

This work relates the theoretical study of the dynamic behavior of a dual free-piston Stirling engine (DFPSE) coupled with an asynchronous linear alternator. This machine integrates one piston and two displacers placed in a symmetrical way compared to the piston to improve the stability of the machine. The paper presents an analytical study of the dynamic balance equations of a DFPSE. This model takes into account the non-linear dissipative effects of the fluid and the electromagnetic forces. The dynamic balance equations of the machine are solved by means of linearized pressure in the time domain especially. The objective is to evaluate the thermo-mechanical conditions for stable operation of the engine. The developed model may be used to simulate the dynamic behaviour of a built engine. The DFPSE produces a mechanical power of 1 kW and it has a design operating point of 1.4 MPa corresponding to the frequency about 22 Hz. Helium is the working fluid. This machine is designed to be used as a micro combined heat and power (μCHP) system for combined generation of electricity and heat.     

Field-test of a solar low delta-T Stirling engine

The ultimate aim of a Moroccan–German study is to develop a simple solar pumping system, using the concept of low delta-T Stirling engines. This paper describes the main parts of the engine and presents several experimental measurements made under laboratory and field-test conditions in Morocco. Measurements with flat plate cooler and discontinuous motion of the displacer were conducted to verify two essential recommendations of Kolin in expectation of power-output improvements of the gamma-type engine.     

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.     

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.     

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.     

Simulation and experimental improvement on a small-scale Stirling thermo-acoustic engine

Compared with the traditional engines, the thermo-acoustic engines are relatively new and can act as the linear compressors for refrigerators. Many institutes have shown great interest in this kind of machine for its absence of moving mechanical part. In this paper, the influence of the dimensions of the main parts of the smallscale Stirling thermo-acoustic engine was numerically simulated using a computer code called DeltaEC. The resonator and the resonator cavity were found to be the most convenient and effective in improving the performance of the engine. Based on the numerical simulation, a small-scale Stirling thermo-acoustic engine were constructed and experimentally investigated. Currently, with a resonator length of only 1 m, the working frequency of the engine was decreased to 90 Hz and the onset temperature difference was decreased to 198.2 K.     

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.