Stirling Refrigerator Research Articles

Energy and exergo-environmental analysis of a refrigerator-Stirling/Photovoltaic system for cold production

The Stirling refrigerator is a device capable of using green energies such as solar power. In this work, a refrigerator-Stirling/photovoltaic system is proposed to harness solar energy for cold production. The system consists of photovoltaic (PV) panels that capture solar energy and convert it into electricity, and a transmission belt linking the motor to the Stirling beta refrigerator to use the electricity for cooling purposes. The system is modeled on the basis of finite-dimensional thermodynamics, taking into account the refrigerator's internal and external irreversibilities. In addition, the wiring loss, dust coverage and shading of the photovoltaic system and the mechanical power loss of the Stirling refrigerator are taken into account in this model. Power equality has been considered as a system constraint. Finally, the effects of operational and design parameters on system performance are investigated. A numerical code is written in Matlab. The effects of PV module efficiency, Stirling regenerator efficiency and PV derating factor on system performance are quantified, also the optimum operating parameters obtained. The refrigerator-Stirling/photovoltaic has a high COP and a low cooling capacity, in contrast to the refrigerator-Stirling/Dish-Stirling. The optimum solar electric COP and maximum cooling rate are 0.7063 and 1413 W respectively at an optimum panel area of 2 m2. Optimum exergy efficiency is 38.5 % at fv = 0.1, ecological coefficient of performance (ECOP) is 20.3 % at N = 48 rot.s−1, optimum exergy destroyed is 33.31 W at K1 = 21.5 W.K−1. This system can be used to preserve vaccines in hospitals.

The pressure-volume relationship in an ideal Stirling refrigerator

Hysteresis losses in the heat transfer between compressing or expanding gas and the adjacent wall is said to play an important role in Stirling machines, where it increases the amount of required p-V work. Previous studies have linked hysteresis loss with the pressure phase shift. In the context of this research, the effect of the pressure phase shift on the net p-V work in a single space is examined.A Sage model of a single space piston-cylinder device is used to investigate the underlying mechanisms of the pressure phase shift. The Sage model is validated using an experimental piston seal rig. In addition, the time dependence of heat transfer is discussed along with how it affects the pressure phase shift, using an iterative model. The Schmidt equations were manipulated to determine the phase shift between pressure and volumetric oscillation in an ideal Stirling refrigerator.The results of this investigation are surprising. It was found that even in the case of an idealized Stirling refrigerator, the phase shift between pressure and volume is non-zero in order to produce a refrigeration effect.

Numerical modelling of thermoacoustic Stirling engines & refrigerators

This paper investigates how numerical modelling can be used to explore thermoacoustic machines and compares the accuracy of the performance predictions for different simulation software. The software used includes one designed for modelling Stirling machines called ‘Sage’ and for modelling thermoacoustic machines called ‘DeltaEC.’ To compare their results, a model of both a thermoacoustic Stirling engine and refrigerator were developed from existing models in published papers, which contained experimental data to validate the numerical models. Overall, it was found that although both can accurately model thermoacoustic machines, they present different optimal conditions, and Sage’s solving method makes it more complex to model the standing wave.

Experimental and numerical study on a heat-driven direct-coupled Stirling refrigerator

As an environmentally friendly refrigeration system, the heat-driven Stirling refrigerator, which has demonstrated high efficiency and promising application prospects, is receiving significant attention for utilizing the waste heat to generate the cooling capacity. In this study, a heat-driven direct-coupled Stirling refrigerator, featuring an engine unit and a refrigeration unit directly coupled through a thermal buffer tube rather than utilizing a piston-based mechanism, is designed and tested. In comparison to the conventional heat-driven Stirling refrigeration systems, the proposed system exhibits the potential for significantly increased reliability and simplicity. Simulations and experiments were carried out to investigate the output characteristics of the system under different heating temperatures and mean pressures. The results show that higher heating temperature is beneficial for producing the acoustic power, thereby increasing the cooling capacity, with the mean pressure among 2.7–3.2 MPa. In the experiments, the system can provide a cooling capacity of 363W with a coefficient of performance of 0.17 when the heating, ambient, and cooling temperatures are 250, 35, and 7 °C, respectively. The results have validated the feasibility of the heat-driven direct-coupled Stirling refrigerator, which is a potential alternative for air-conditioning through waste-heat recovery.

Numerical Modelling of Thermoacoustic Stirling Engines & Refrigerators

Thermoacoustic machines depend on the complex relationship between thermodynamics and acoustics, and thus understanding it is vital in order to analyse the working principles and optimise parameters (i.e. geometrical or operational) to improve their performance. This paper investigates how numerical modelling can be used to explore this relationship and compares the accuracy of the performance predictions for different numerical simulation software. The software used included one designed for modelling Stirling machines called ‘Sage’ and one designed for modelling thermoacoustic machines called ‘DeltaEC’. To compare their results a model of both a thermoacoustic Stirling engine and refrigerator were developed from existing models in published papers, which contained experimental data to validate the numerical models. The results from the thermoacoustic Stirling engine model show that there is good agreement between the predictions from DeltaEC and the experimental data, as well as relatively good agreement between the Sage and DeltaEC predictions. However, due to Sage requiring a different approach to model the boundary conditions for the standing wave type machine (i.e. one end closed) the predictions varied slightly from those by DeltaEC. The results from the thermoacoustic Stirling refrigerator model, however, show improved agreement between the predictions from Sage and DeltaEC – potentially due to Sage and DeltaEC using a similar approach to model the boundary conditions for the travelling wave type (i.e. two open ends). Overall, it was found that although both can accurately model travelling wave thermoacoustic machines, the nature of Sage’s solving method makes it more complex to model the standing wave type compared to DeltaEC. A discussion on the use of numerical models as a tool for better understanding thermoacoustic machines, and the importance of the accuracy of the results to allow for optimisation and improvement in their design is presented.

Development of the double two-phase thermosyphon loops used in low temperature Stirling refrigerator

With the growing of demand for the low temperature pharmaceutical cold chain, the Stirling cooler has been attractive for years. However, the heat transfer inside the refrigerator could be ineffective by natural convection due to the small area of the plug-in Stirling cold finger. In this paper, the double two-phase thermosyphon loops (DTPTLs) used for low temperature Stirling refrigerator is developed. The characterization of heat transfer and pressure drop in the DTPTLs is investigated by theoretical calculation for various working refrigerants. Then the basic structure of the DTPTLs is modified and improved for dragging and moving convenience. Moreover, the comparison of the temperature distribution inside the refrigerator container between the DTPTLs and the plug-in cold finger methods is demonstrated by numerical simulation. The simulation result indicates that a well temperature distribution inside the container can be obtained by using DTPTLs. In the end, an experimental test is conducted at room temperature. It's shown that the no-load cooling temperature could reach −80 °C in a few minutes. Over steady-state operation, the maximum temperature difference all inside the container is less than 5 °C, which proved the positive heat transfer effect of the DTPTLs on the cooling performance of the low temperature Stirling refrigerator system.

Parametric Investigation and Univariant Optimization of Domestic Stirling Refrigerator

As the temperature range of the cooling machine affects the cooling performance, parametric optimization of moderate temperature Stirling refrigerator has valuable concept. In this paper, a nonideal modified simple numerical model was used to investigate the effects of parameters and to propose optimized Stirling refrigerator design for moderate temperature applications. The analysis was conducted through simulating the numerical model using MATLAB code for beta configuration FEMTO-60 prototype operating as a refrigerator. The effects of shuttle heat loss and mass leakage on the cooling performance of domestic Stirling refrigerator have been studied. Moreover, the effects of operating parameters (operating frequency and charging pressure) and design parameters (phase angle, regenerator length and porosity, displacer height, swept volume ratio, and piston diameter to stroke ratio) have been investigated. A cooling power of 625 W and COP of 1.3 have been found at a charging pressure of 22.5 bar and an operating frequency of 6 Hz using the optimized design parameters. The optimized parameters (operating and specified design parameters) could deliver from 48% to 60% more cold production and from 30% to 40% more COP than the existing design with a safe working condition.

Ionocaloric refrigeration cycle

Developing high-efficiency cooling with safe, low-global warming potential refrigerants is a grand challenge for tackling climate change. Caloric effect-based cooling technologies, such as magneto- or electrocaloric refrigeration, are promising but often require large applied fields for a relatively low coefficient of performance and adiabatic temperature change. We propose using the ionocaloric effect and the accompanying thermodynamic cycle as a caloric-based, all-condensed-phase cooling technology. Theoretical and experimental results show higher adiabatic temperature change and entropy change per unit mass and volume compared with other caloric effects under low applied field strengths. We demonstrated the viability of a practical system using an ionocaloric Stirling refrigeration cycle. Our experimental results show a coefficient of performance of 30% relative to Carnot and a temperature lift as high as 25°C using a voltage strength of ~0.22 volts.

A novel cryogenic condensation system combined with gas turbine with low carbon emission for volatile compounds recovery

The issue of volatile organic compounds (VOCs) is a global concern due to its significant influence on environmental pollution, climate change, and human health. Condensation is an available VOCs recovery method, but it currently has obvious shortcomings in terms of energy consumption, carbon emissions, refrigerants, and emission concentration. In this paper, a novel VOCs condensation system combined with gas turbine was proposed. The heat obtained by burning part of the exhaust gas is employed to drive an absorption refrigerator using ammonia water and a Stirling refrigerator using helium to recover VOCs contained in the remaining exhaust gas, which has the advantages of not requiring an external power supply, low carbon emissions, using natural refrigerant and nearly zero-VOCs emission. In order to obtain the optimal recovery efficiency, a thermodynamic calculation model was established, and related experimental verifications were carried out. The results show that the remaining 93.3% of the VOCs can be recovered by burning 6.7% of the VOCs when the absorption refrigerator (213 K) recovers the waste heat of the gas turbine used to power the Stirling refrigerator (110 K). The carbon emission reduction efficiency is as high as 92.9% and the carbon emission reduction is 16707 tons per year. The effects of the refrigeration temperature, heat source temperature, gas turbine efficiency, refrigerator efficiency and exhaust gas flowrate on the recovery efficiency were also analyzed.

A Potential Method to Predict Performance of Positive Stirling Cycles Based on Reverse Ones

There are two kinds of working mechanisms for the Stirling cycle, i.e., the positive and the reverse cycles, and a Stirling engine (SE) can be operated as a Stirling refrigerator (SR). This indicates that a probable practical method for evaluating the performance of a Stirling engine is to run it as a refrigerator, which is much easier to operate. For this purpose, an improved Simple model for both the positive and the reverse Stirling cycles, considering the various loss mechanisms and actual operating conditions, is proposed and verified by a self-designed Stirling engine. As to the positive cycle with helium and nitrogen at 2.8 MPa, the model errors range from 5.4–11.3% for the indicated power, and 1–10.2% for the cycle efficiency. As to the reverse cycle with helium and nitrogen, the errors of the predicted input power range from 7.9–15.3% and from 2.5–10.9%, respectively. The experimental cooling temperatures can reach −92.2 and −53.6 °C, respectively, for the reverse cycle with the helium and nitrogen at 2.8 MPa. This Stirling-cycle analysis model shows a good adaptability for both the positive and the reverse cycles. In addition, the p-V maps of the positive and reverse cycles are compared in terms of “pressure ratio” and “curve shape”. The pressure ratio of the reverse cycle is significantly higher than that of the positive one at the same mean pressure. A method is proposed to predict the indicated work of the positive Stirling cycles using the reverse ones. A mathematical model to predict the indicated power of the positive Stirling cycles based on the reverse ones is proposed: Wheat2−Wcool1=A·(Tge2−Tgc2Tgc1−Tge1)B. The most critical issue with this method is to establish an associated model of the temperatures of the expansion and the compression space. This model shows a good adaptability for both the positive and the reverse cycles and can provide detailed information for deep discussion between the positive and the reverse cycles.

A non-ideal second order thermal model with effects of losses for simulating beta-type Stirling refrigerating machine

A key issue in the optimal designing of a Stirling machine is to develop a precise thermodynamic numerical model that could predict the performances and provide means for further optimization. In this paper, a non-ideal second-order numerical model called modified simple analysis model has been presented for the Stirling cycle refrigerating machine. The model incorporates effects of shuttle heat loss to the expansion space and mass leakage to the crankcase in the differential equations of pressure change, rate of change of mass of gas in compression and expansion spaces, and mass flow rates across these working spaces. The model was simulated using MATLAB code for Beta configuration FEMTO 60 Stirling engine operating as a refrigerator and validated with an experiment. The validation of the numerical model with experimental work showed that the results of the simulation are consistent with the results of the experiment. Hence, the numerical model could be used to design a Stirling cycle refrigerating machine for moderate temperature applications with reasonable accuracy especially if optimization is performed further. The effects of incorporating shuttle heat loss in the differential equations on the temperature of working gas and the overall performance of the Stirling refrigerator have been analyzed. Lastly, parametric investigations have also been performed to evaluate the effect of operating parameters (temperature, pressure, and frequency) on the performances of the refrigerating machine. Better performance could be achieved at relatively lower frequency or higher pressure.

Numerical investigation on a heat-driven free-piston thermoacoustic-Stirling refrigeration system with a unique configuration for recovering low-to-medium grade waste heat

• A novel heat-driven free-piston thermoacoustic Stirling cooling system is proposed. • The direct-coupling and single displacer configuration is introduced in the system. • The influences of various operating conditions are systematically analyzed. • It can achieve a COP above 0.60 below a heating temperature of 300°C. In this paper, a unique heat-driven free-piston thermoacoustic-Stirling refrigeration configuration is proposed to effectively provide room-temperature cooling by using low/medium-grade waste heat. Compared with the traditional duplex free-piston Stirling refrigerator, the unique feature of the proposed novel configuration is that it has only one single moving displacer and uses a thermal buffer tube to directly couple a thermoacoustic heat engine and a refrigerator, consequently leading to higher reliability and compactness. Numerical simulation and analysis have been conducted, focusing on the acoustical and thermodynamic characteristics as well as its global cooling performance. The thermoacoustic characteristics of the system are analyzed in details to understand its operating mechanism and cooling performance. Additional analyses are focused on the influences of the heating temperature and the working pressure on the thermodynamic performances of this system. A 2kW-class case study for air-conditioning refrigeration application shows that it can achieve a COP (coefficient of performance) of more than 0.62 at a refrigeration temperature of 10°C, under the conditions of an ambient temperature of 50°C and a heating temperature of 300°C. Its compactness and high efficiency are very competitive to the current heat-driven refrigerators, showing great potential in compact air-conditioning application by utilizing low-to-medium grade waste heat sources.

Beta Stirling refrigerator performance using a tubular heat exchanger with elliptical tube layouts and a cylinder with different bores

Beta Stirling refrigerator performance using a tubular heat exchanger with elliptical tube layouts and a cylinder with different bores

A novel Gamma‐type duplex Stirling system to convert heat energy to cooling power: Theoretical and experimental study

This article aims at coupling two Stirling machines together to produce cooling power from different heat sources. Two identical Gamma-type ST500 Stirling machines are coupled together. The first machine, named Stirling engine, is powered by burning natural gas and an electrical power supply as an auxiliary starter. The Stirling engine is connected to a second Stirling machine named Stirling refrigerator by a mechanical belt. The driving force is transferred to the Stirling refrigerator using the mechanical belt. Mechanical energy is then converted to cold energy in the Stirling refrigerator. This study presents the experimental and theoretical results by examining the whole system named duplex Stirling refrigerator system. Five experiments are performed on the system at different pressures to evaluate the results. Water circulation in copper coils is used to determine the cooling flux produced by the Stirling refrigerator. Finally, the coefficient of performance (COP) is calculated. The experimental data are validated using a MATLAB-based code developed based on the presented formulas in this study. The results show that the system's maximum COP and electrical efficiency, consisting of two similar 500 W Gamma-type Stirling machines, are between 0.21% and 70.8%, respectively. Setup theoretical and experimental efficiencies are 0.24 and 0.21, respectively, at the best case. The experimental results of the duplex Stirling refrigerator system used in this study are compared with the simulation results. Finally, the experimental results of this study are compared with some other reported results from different authors on the subject of the duplex Stirling refrigerator.

Stirling Refrigerating Machine Modeling Using Schmidt and Finite Physical Dimensions Thermodynamic Models: A Comparison with Experiments

The purpose of the study is to show that two simple models that take into account only the irreversibility due to temperature difference in the heat exchangers and imperfect regeneration are able to indicate refrigerating machine behavior. In the present paper, the finite physical dimensions thermodynamics (FPDT) method and 0-D modeling using the Schmidt model with imperfect regeneration were applied in the study of a β type Stirling refrigeration machine.The 0-D modeling is improved by including the irreversibility caused by imperfect regeneration and the finite temperature difference between the gas and the heat exchangers wall. A flowchart of the Stirling refrigerator exergy balance is presented to show the internal and external irreversibilities. It is found that the irreversibility at the regenerator level is more important than that at the heat exchangers level. The energies exchanged by the working gas are expressed according to the practical parameters, necessary for the engineer during the entire project. The results of the two thermodynamic models are presented in comparison with the experimental results, which leads to validation of the proposed FPDT model for the functional and constructive parameters of the studied refrigerating machine.

Investigation of thermal and fluidic losses and their effect on the performances of a Stirling refrigerator

The design of a Stirling machine requires the understanding of the processes that govern their operation to predict the optimum operating parameters of the machine. The modified simple model using the geometrical parameters of the FEMTO-ST engine model is applied in this paper to investigate the trend of losses with respect to operating frequency and charging pressure. The variation of pressure drops across the regenerator and heat exchangers have been investigated as functions of operating frequency and charging pressure in order to predict the extent of fluid friction losses. The share of different power and heat losses as well as their effects on cooling performance have been evaluated at the different operating frequencies and charging pressures. The share of fluid friction loss and loss due to regenerator imperfection increase with rotational speed and charging pressure.

A combined cooling and power cogeneration system by coupling duplex free-piston stirling cycles and a linear alternator

Abstract We propose a novel cooling and power cogeneration system based on duplex free-piston thermoacoustic-Stirling cycles and an oscillating linear alternator. In such a cogeneration system, a free-piston Stirling heat engine produces acoustic power via the thermoacoustic power cycle, and a free-piston Stirling refrigerator produces cooling power via the thermoacoustic refrigeration cycle; an oscillating linear alternator is used to couple the free-piston heat engine and refrigerator and simultaneously produces electricity. The configuration and operating principles of the cogeneration system are described along with the thermoacoustic energy transformations and transmission mechanisms. An experimental prototype system was designed, built and successfully operated for the first time. In the preliminary experiments, thermoacoustic oscillation startup typically occurred at heating temperatures around 50 to 60 °C, and a cooling power of about 230 W at -20 °C and an electrical power of more than 6 W were obtained at a heating temperature below 190 °C. The alternator-coupled system has potential applications in heat-driven cogeneration systems for low-grade waste heat recovery and solar energy utilization.

Assessment of design constraints for the Duplex Stirling Refrigerator with imperfect regeneration

Duplex Stirling refrigerators are the alternative cycles to the conventional vapor refrigeration cycles with their high efficient, low noise, and low emission characteristics. It consists of a Stirling heat engine and a Stirling refrigerator in a mono-block construction that operates by a power piston. In this particular study, the effect of imperfect regeneration on the performance of the duplex Stirling refrigerator is determined analytically while helium is the working fluid. The polytropic heat transfer processes are chosen instead of isothermal processes to get a more realistic approach. Various temperature and compression ratios are taken into account for the refrigerator side of the duplex system and the required compression ratio of the heat engine is determined by using the work equality constraint. The combined effects of the regenerator effectiveness, temperature and compression ratios on the performance of the duplex system are assessed. The results of the parametric analysis are presented in terms of heat removal from the refrigerated space, coefficient of performance of the refrigerator side, work consumed by the system, heat addition to the engine side, thermal efficiency and overall system performance.

Effect of expander shape on cooling characteristics by using a model pulse tube refrigerator

Pulse tube refrigerators do not have moving parts in the cold section, and they have low vibration, high reliability, and long life. The expander in refrigerators typically has an inverted U or coaxial shape because this attains a wider absorber area, lower height, and compactness. However, the performance of a Stirling-type pulse tube refrigerator is inferior to that of a Stirling refrigerator. Cooling characteristics of the pulse tube refrigerator greatly depend on the shape of the expander. In this study, an inertance-type refrigerator, which uses ambient air for the working gas, was developed to examine the effect of expander shape. This refrigerator model with changeable expander operated with a Stirling cycle, and it was composed of a reciprocating compressor, after-cooler, regenerator, absorber, pulse tube, hot-end, and inertance tube with reservoir. The following expander shapes were tested: in-line, L shape, L-L shape, and coaxial shape. The effect of expander shape on cooling capacity was examined experimentally and numerically using the model pulse tube refrigerator. The results of experiments showed that the L shape expander had the highest performance and the coaxial expander had the lowest performance. In addition, the characteristics of the gas flow in each expander were confirmed by fluid dynamics analysis.

Progress of the 4 K-class Vuilleumier type cryocooler and its further applications

Vuilleumier cycle was first patented in 1918. It was usually regard as the thermal-driven Stirling refrigeration cycle, which combined the low-frequency working pattern like Giffod-Mcmahon (GM) cryocooler and the compactness of Stirling-type cryocooler. With the continuous development in the past 100 years, the Vuilleumier-type (VM-type) cryocoolers have to been proved to generate cooling power from ambient temperature to liquid nitrogen temperature and even to liquid helium temperature. In recent decades, some efforts were made on traditional displacer-type VM cryocooler, Vuilleumier hybrid pulse tube cryocooler (VM-HPTC) and the VM-type pulse tube cryocooler (VM-type PTC) to obtain the liquid helium temperature. Successfully, not only the 4 K was obtained, but also the limit temperature of oscillating cryocooler by He4 was hit. This paper presents the progress of the 4 K-class VM-type cryocooler and analyzed the possible applications of 4 K class VM-type cryocooler.