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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.

The Stirling cycle machines have many applications as prime mover and cooling purpose. A review is presented for the development of regenerative Stirling cycle machines in the refrigeration area. The Stirling cycle refrigerators of gas cycle machines, which are the counterparts of the Stirling engines. They can operate from low temperature to moderate temperature applications. The present paper describes an overview of the Stirling refrigerating machine and its associated researches carried out in this area.Initially, the review explains the general working principle, the configuration and the drive mechanisms as well as the research findings within the range from low-temperature cryocoolers to moderate temperature cooling applications. Furthermore, this review points out and discusses the various models and methods of optimization to improve the performance of the Stirling cycle refrigerator.

International audience; As the concern for CO2 emissions and global warming raises, the Stirling machine appears as a candidate alternative technology to vapor compression cycles that use refrigerant fluids. In this paper, we present the design, manufacturing and testing of a Beta Stirling machine for refrigeration applications. The first part of the paper presents the principle of the Stirling cycle, the mechanical configuration of the designed machine, and the key design parameters. The second part describes the experimental test bench and instrumentation of the Stirling machine. The last part of the paper presents experimental results. The prototype typical performance is a 450 W heat lift at 4°C and a COP of 0.9 when Nitrogen is used as the working gas. Cold end temperature variation as a function of heat lifts and charge pressure are presented. Coefficient of Performance is also discussed. Mechanical power, instantaneous torque and velocities curves are reported.

International audience; In this paper, we present a new model design and parametric studies of a miniature Stirling cooler machine for on-site refrigeration. The MEMS (Microelectromechanical systems) technology is investigated to design this machine. The concept could be used to provide cooling at chip scale and mitigate hot spots in electronic devices. Whereas numerous works deal with Stirling engines at a macroscopic scale, only a few works concern miniaturized Stirling engines. Therefore, a model analysis giving insights of the impact of the technological choices and downsizing of the machine is needed. A base design model is presented. The model results lead to a cooling power of 10 mW and a Coefficient Of Performance of 1.45. A parametric study is conducted for operational and design parameters. Compared to macro-scale design, the same trend is observed for the influence of the thermal performance regenerator. Different trends from macroscopic engines were observed for hysteresis losses importance, and the choice of the working gas. The raise in power due to the raise in frequency expected for micro-scale devices is counterbalanced by the degradation of the COP due to the increase in thermofluidic losses. Squeeze film damping and finite speed losses can be neglected at this scale.

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.

The Stirling cycle refrigerators, which are the counterparts of the Stirling engines are of gas cycle machines. In the present paper, experimental investigation and numerical analysis of Beta-type Stirling refrigerator for domestic applications are conducted. The refrigeration performances such as input power requirement, cooling power, and coefficient of performance for moderate temperature applications have been analyzed using different working fluids (air, nitrogen, helium, and hydrogen). The numerical analysis is conducted to evaluate the performance of a machine with respect to different operating frequencies and charging pressures. The result of the analysis showed that air and nitrogen have better cooling power than helium and hydrogen in the operating ranges (15–25 bar and 6–12 Hz) of the cooling machine. On the other hand, the coefficient of performances in the case of helium shows a higher rate of increase with charging pressure than that of air and nitrogen.

A regenerator of a Stirling machine alternately absorbs and releases heat from and to the working fluid which allows to recycle rejected heat during theoretical isochoric processes. This work focuses on a milli-regenerator fabricated with a multiple jet molding process. The regenerator is a porous medium filled with a dense pillar matrix. The pillars have a geometrical lens shape. Two metallic layers (chromium and copper) are deposited on the polymer pillars to increase heat transfer inside the regenerator. We performed experiments on different milli-regenerators corresponding to three porosities (ε = 0.80, 0.85 and 0.90) under nitrogen steady and oscillating compressible flows (oscillating Reynolds number in the range 0 < Reω < 60 and Reynolds number based on the hydraulic diameter ReDh,maxT < 100°C). Temperature, velocity and pressure experimental measurements are performed with microthermocouples (type K with 7,6 µm diameter), hotwires and miniature pressure sensors, respectively. We identified a threeterm composite correlation equation for the friction factor based on a Darcy-Forchheimer flow model that best-fit the experimental data. In steady and oscillating flows permeabilities and inertial coefficients are of the same magnitude order. Inertial coefficients decrease when the porosities increase.

International audience; In this paper, we present a new model and design of a MEMS Stirling machine. The concept could be used to provide electricity to low level power systems. A modified adiabatic model including losses of a Stirling engine such as regenerator thermal efficiency, wall conduction, pressure drop, hysteresis, membrane finite speed and squeeze film damping losses is presented. A base design machine is proposed. A parametric study is conducted and used to derive guidelines for miniature design. Compared to macro-scale design, the same trend was observed for the influence of the thermal performance regenerator. However, different trends from macroscopic engines were observed: conduction losses are of major importance due to the low power of the miniature engines, hysteresis losses in the bounce space are also of high amplitude due to the small size if this volume, the choice of the working gas leads to hydrogen or air and not helium. We computed that membrane finite speed losses and squeeze film damping losses can be neglected in the investigated machine size. The first part of the paper presents the micro-machine specific features, the second part describes the model, the last part presents the base design results and design guidelines.

The second law of thermodynamics is applied to evaluate the influence of entropy generation on the performances of a cold heat exchanger of an experimental Stirling refrigeration machine by means of three factors: the entropy generation rate N S , the irreversibility distribution ratio ϕ and the Bejan number B e | N S based on a dimensionless entropy ratio that we introduced. These factors are investigated as functions of characteristic dimensions of the heat exchanger (hydraulic diameter and length), coolant mass flow and cold gas temperature. We have demonstrated the role of these factors on the thermal and fluid friction irreversibilities. The conclusions are derived from the behavior of the entropy generation factors concerning the heat transfer and fluid friction characteristics of a double-pipe type heat exchanger crossed by a coolant liquid (55/45 by mass ethylene glycol/water mixture) in the temperature range 240 K &lt, TC &lt, 300 K. The mathematical model of entropy generation includes experimental measurements of pressures, temperatures and coolant mass flow, and the characteristic dimensions of the heat exchanger. A large characteristic length and small hydraulic diameter generate large entropy production, especially at a low mean temperature, because the high value of the coolant liquid viscosity increases the fluid frictions. The model and experiments showed the dominance of heat transfer over viscous friction in the cold heat exchanger and B e | N S &rarr, 1 and ϕ &rarr, 0 for mass flow rates m ˙ &rarr, 0.1 kg.s&minus, 1.

International audience; In this paper, we present an experimental study on the pressure, pressure drop, velocity and friction factor in a regenerator made from an array of pillars in reciprocating flow conditions. The fluid used in the experiment is air. We show that the pressure drop depends on the porosity, frequency and stroke. We observe a phase shift between the crank angle sinusoidal variation of the piston and the pressure variation that increases with frequency. We also observe that the instantaneous friction factor is higher in the discharge phase than in the suction phase, and higher in the acceleration than in the deceleration phase. Friction factor in oscillating flow appears to be higher than friction factor in steady unidirectional flow for the highest porosity. For the lower porosities, we observe that the pressure drop and friction factors are similar for maximum Reynolds numbers lower than 5000. An experimental correlation for the friction factor of the regenerator is derived in order to design a millimetric Stirling engine. The friction factor is compared with friction factors reported for woven screens, metal felts and involute foil regenerators.

International audience; This paper describes a Stirling Engine used as an Auxiliary Power Unit in a Series Hybrid Vehicle. The engine modeling is presented, then its integration in the vehicle power train is described. Fuel consumption, power train efficiency are compared between Stirling Engines and Spark ignition Engines. The results show that Stirling engines present good performances compared to internal combustion engines in the same configuration. Finally, the prototype design and first results are presented.

The implementation of Fuel Cell (FC) systems in transportation systems, as aircrafts, requires some better understanding and mastering of the new generator behaviours in low temperature environments. To this end, a PEMFC stack is tested and characterised in a climatic chamber. The impacts of the low temperatures over different FC operation and start-up conditions are estimated using a specific test bench developed in-lab. Some descriptions concerning the test facilities and the experimental set-up are given in the paper, as well as some information about the test procedures applied. Some examples of test results are shown and analysed. The experiments are derived from aircraft requirements and are related with different scenarios of airplane operation. Finally, some assessments concerning the FC system behaviour in low temperature conditions are made, especially with regard to the constraints to be encountered by the next embedded FC generators.

International audience; Fuel cell self start at negative temperature conditions is not an easy task due to the water produced by the reduction of oxygen at the cathode. This amount of water can turn into ice and block the reaction before the temperature inside the fuel cell reaches positive values. The mechanism of the physical process which leads to oxidant starvation phenomena when ice appears is not yet well identified. In order to obtain a deeper understanding of this problem, the article presents some experimental investigations conducted on a short fuel cell stack. These experiments simulate vehicle technology operated in cold start conditions not with the primary objective to reach a successful and rapid start-up but much rather to characterise and understand the cold start phenomena until starvation occurs. A number of polarisation curves, electrochemical spectroscopy and cyclic voltammetry measurements are done on the stack before, after and also during the cold starts experiments. It is observed that the process of drying and cooling down prior to cold start have a great impact on the electrochemical cathode area. The results obtained show the evolution of the stack behaviour during the low temperature operation with a slow production of frost. The consequence on the individual cells in terms of inhomogeneous degradation is highlighted.

This paper presents a stability analysis of a free piston Stirling engine. The model and the detailed calculation of pressures losses are exposed. Stability of the machine is studied by the observation of the eigenvalues of the model matrix. Model validation based on the comparison with NASA experimental results is described. The influence of operational and construction parameters on performance and stability issues is exposed. The results show that most parameters that are beneficial for machine power seem to induce irregular mechanical characteristics with load, suggesting that self-sustained oscillations could be difficult to maintain and control.