The paper presents design and preliminary testing results of a Free Piston Stirling Engine (FPSE) prototyp operating at low temperature heat sources. The main focus of this work is to demonstrate the construction of the displacer using flexure bellows as a mechanical supporting spring and as a working fluid seal. The power piston, on the other hand, is made of a planar elastomer material in the shape of a disk with a suitable mechanical elasticity, rigidity, and thermal properties to support the range of operating temperatures. A small prototype of the FPSE was built and tested at operating temperature of under 200 oC. The measured operating frequency was 15 Hz, a reciprocating stroke of 8mm and operating pressure close to atmospheric pressure. The prototype was equipped with instruments to measure all the operating parameters. The power output was measured from the p-v diagram using a two-channel oscilloscope. The preliminary results demonstrated the operation concept and reliable start up, but further improvements will be needed to fine tune the reciprocating components and reduce mechanical friction

Boukhanouf, Rabah

Ghozzi, Salem

Name not available

Preliminary testing results of a diaphragm FPSE

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Ghozzi, Salem and Boukhanouf, Rabah (2016) Preliminary testing results of a diaphragm FPSE. In: 7th Heat Powered Cycles Conference (HPC 2016), 26-29 June 2016, Nottingham, UK. Access from the University of Nottingham repository: http://eprints.nottingham.ac.uk/34489/1/HPC580%20-%20Salem%20and%20Rabah%20paper.pdfCopyright and reuse: The Nottingham ePrints service makes this work by researchers of the University of Nottingham available open access under the following conditions.This article is made available under the University of Nottingham End User licence and may be reused according to the conditions of the licence.  For more details see: http://eprints.nottingham.ac.uk/end_user_agreement.pdfA note on versions: The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher’s version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.ukPRELIMINARY TESTING RESULTS OF A DIAPHRAGM FPSESalem Ghozzi and Rabah BoukhanoufDepartment of Architecture Built Environment, Faculty of engineering, University of Nottingham, Nottingham, NG7 2RD, UKABSTRACTThe paper presents design and preliminary testing results of a Free Piston Stirling Engine (FPSE)prototype operating at low temperature heat sources. The main focus of this work is to demonstrate theconstruction of the displacer using flexure bellows as a mechanical supporting spring and as a workingfluid seal. The power piston, on the other hand, is made of a planar elastomer material in the shape of adisk with a suitable mechanical elasticity, rigidity, and thermal properties to support the range ofoperating temperatures. A small prototype of the FPSE was built and tested at operating temperature ofunder 200oC. The measured operating frequency was 15 Hz, a reciprocating stroke of 8mm and operatingpressure close to atmospheric pressure. The prototype was equipped with instruments to measure all theoperating parameters. The power output was measured from the p-v diagram using a two-channeloscilloscope. The preliminary results demonstrated the operation concept and reliable start up, but furtherimprovements will be needed to fine tune the reciprocating components and reduce mechanical friction.KEYWORDSFree piston Stirling engine, metal bellow, and diaphragm1 INTRODUCTIONEnergy is one of the key challenging issues that both industrialized and developing nations will have toface in the future to sustain the economic development and social wellbeing for their population.According to World Bank estimates, around 1.6 billion people worldwide do not have access to electricity;due to limited power grid infrastructure extension into rural areas where most of the population indeveloping countries lives. Rural electrification helps to improve living conditions and reduce healthproblems born from burning primitive fuels in inadequate appliances. In many instances, however,existing electricity grids in developing countries are either not extended to remote rural areas and/orcannot supply enough electrical power to guarantee stable operation of the grid due to high investmentand maintenances costs [1]. This is most acutely demonstrated in sub-sahara africa and some parts ofsouth asia where access to electricty is as low as 10% and 13% respectively [2]. Adoption of off-gridsustainable power generators is one of critical technologies with many applications including cropsirrigation, medicine preservation through cooling, lighting, etc. to enhance people lives in isolate ruralregions of the developing countries and limit migration into big cities.The focus in this work is to develop a cheap free piston Stirling engine that can be power by solar energyand afforded by small farmers in developing countries for water irrigation applications to increaseagricultural productivity to meet food needs of a growing population.A Stirling Engine is an external combustion heat engine that can operate on virtually any source of heat toproduce shaft power provided a sufficiently temperature difference exists between the he heat source andheat sink. Mechanically, the engine is simple with few moving components. The development of Stirlingengines have been dampened by the success of internal combustion engines which have superior specificpower output, reliability and lower in manufacturing cost.2 MECHNAICALDESIGNAND CONFIGUATIONA simplified mechanical layout of the Free Piston Stirling engine is shown in Figure 1. It consistsparticularly of an integrated displacer-bellows assembly housed in the cylinder and separates the heatsources and the heat sink. The displacer-bellows assembly is hollow and light structure that forms asuspended mass-spring oscillating components with no friction with the cylinder. The narrow passagebetween the displacer and cylinder allows air flow between the hot side and cold side while the bellowsconvolutions (extended surface area) form the regenerator.The working space of the engine is sealed by a power piston in the form of a flexible material flat disk(diaphragm) of suitable hardness grade and which acts as the power piston. The flexible power pistonforms a second resonating assembly with the shaft load. A small pressure gradient across the displacerexerts a force that sustains the displacer oscillation and hence the shuttling of the working fluid betweenthe hot and cold end which in turn generates a pressure change in the engine and drives the diaphragmpower piston.Figure 1: Mechanical arrangement of FPSEOne design issue that needs to be overcome is the life span of the oscillating components – bellows anddiaphragm. There is considerable progress in materials technology that makes it possible to operateflexible structures for large number of cycles before failure.In a Stirling engine heat is supplied externally and transferred to the working fluid in the enclosed spacethrough the heater head wall. Using a solar concentrator to focus direct solar rays onto the heater headwould supply heat at required operating temperature. Heat rejection is through a natural convictionradiator on the cold end.2.1 Design of the oscillating componentsThe displacer and diaphragm form the main oscillating mechanical parts of the engine without physicallinkage between the two. For the engine to operate successfully, the displacer and power piston have to betuned to operate at the design frequency. This requires considering carefully the effect of friction, workingfluid damping and the stiffness of the flexure mountings on each component.2.1.1 DisplacerThe displacer is assembled form two components, a rigid cylinder and a supporting flexible bellows. Therigid part is composed of two rigid lightweight cylinders with different cross sectional areas. The differentin cross sectional areas between the top and bottom part of the displacer allows creating a force imbalanceand oscillation at low-pressure variation levels. The displacer-bellows assembly is mounted on a flangewhich in turn is bolted to the main outer cylinder of the engine. Figure 2 shows a general outline of thedisplacer.Figure 2: The displacer assemblyIn sizing the displacer parts, it was important to use off the shelve bellows and stainless steel cylindersand of standard dimensions. However, the selection of the bellows needs to satisfy the required stroke,oscillation frequency and dynamic stability to avoid wobbling and swerving under dynamic forces.Among the parameters to be selected include the bellows inner and outer diameter, the number ofconvolution (height), stiffness of the material and deflection [3].The natural frequency of oscillation of the displacer-bellows assembly depends on the assembly mass andthe bellows overall stiffness. This expressed as:[1]Where the bellows stiffness, k, is proportional to the stiffness of one convolution and inverselyproportional to the total number of convolutions (i.e., ) with kn: is the convolution spring rate(N/m), nw: is the number of the convolutions.The displacer assembly main dimensions are given in Table 1.Table 1: The displacer dataBellow type/materialOperating frequencyOperating pressureOD/IDNumber of convolutionsNominal free lengthAxial strokeNominal stiffness rateLife cycleEdge-welded stainless steel bellows̴̴ 15 Hzatmospheric95 / 76 mm1524 mm±5 mm10 N/mm100,000 (axial movement)2.1.2 Power pistonThe power piston was formed from a flat flexure diaphragm clamped at its circumference. thin diaphragmare widely used in microelectromechanical systems (MEMS) and transducers [4]. A diaphragm powerpiston offers simplicity; complete sealing of the working fluid in the engine, no friction, and long life.Figure 3 illustrates the structure of the diaphragm where it is clamped around its circumference and free atthe centre. A rigid mass is added to the centre of the diaphragm to increase the volume swept and finetune the natural oscillation frequency.Figure 3: Flexure diaphragmThe diaphragm was made of a 6 mm thick and 100 mm diameter flat rubber diaphragm. The maximumdeflection of the diaphragm occurs at its centre and is approximately proportional to the magnitude ofpressure gradient in the engine sealed space. This can be expressed as follows [5]:[2]Where, r and t are the diaphragm radius and thickness, E and are diaphragm material Young’smodulus and Poisson’s ratio, and p is applied pressure over the surface of the diaphragm.The operating service of the diaphragm is measured by the number of oscillation it can produce before failure.This depends strongly on the stress and strain forces applied to the diaphragm material and limiting themaximum stress to below the material’s threshold stress will produce an infinite number of oscillations. Themaximum stress (radial and tangential) applied to the diaphragm at full deflection occur at the clamped edgepart, which is given by:[3]Similarly, the operating frequency of the diaphragm was approximated by the fundamental naturalfrequency of oscillation of a vibrating circular plate with clamped at its edge, as follows [5]:[4]The effect of the surrounding working fluid and clamping arrangement however reduces the oscillatingfrequency. To tune the diaphragm natural frequency, a corrective rigid mass is attached to the diaphragm at itscentre.3 THETESTRIGANDPRELIMINARYRESULTSA small proof of concept prototype diaphragm Stirling engine was built and testing is ongoing. Figure 4illustrate a photograph of the engine test rig.Figure 4: Engine housing casingStarting the engine for the first time proved challenging as a number of design parameters need to be setcorrectly. In addition to satisfying the thermal parameters, the dynamic behaviour of the oscillating partsmust be finely tuned including overcoming frictional and viscous damping forces as well as correcting thenatural frequencies of the components. After the initial modifications, the engine self-starts reliably onapplication of sufficient temperature gradient between the heat source and the heat sink. Figure 5(a)shows the initial attempts at starting the engine where it shows that the diaphragm oscillation decay aftera few oscillations. Eventually, the engine oscillation was sustained at a heat source temperature of about250oC and heat sink temperature of 40 °C. The operating frequency of the engine was measured at 15.4Hz and a diaphragm stroke of 10 mm, as shown in Figure 5(b).Figure 5: Diaphragm oscillation a) decaying oscillation b) sustained oscillationThe testing of the engine is still on-going and further recordings of compression space pressure andvolume variation are shown in Figure 6. It can be seen that the two sinusoidal waveforms are have aphase shift angle of about 80owith pressure lagging.Figure 6: compression space pressure and swept volume variationThe power output of the engine was evaluated from the p-v diagram recording using a digital oscilloscopeis shown in Figure 7. The pressure variation was determined using a pressure transducer and the volumeswept from an LVDT that measures the diaphragm oscillation amplitude. It was estimated that the areaenclosed by the p-v diagram amounts to a power output of about 0.10 W.Figure 7: p-v diagram recording4 CONCLUSIONA FPSE using a flexure bellows and elastomeric material diaphragm was designed and tested. Thepreliminary results demonstrate good operation stability and self-start up operation. Further work will beimplemented to increase the power output through further tuning and enhancing heat regeneration. A loadusing diaphragm type water pump will also be tested for irrigation purposes.REFERENCES[1] Bahaj, A. (2009). Delivering developing country growth: A new mechanistic approach driven bythe photovoltaic industry. Renewable and Sustainable Energy Reviews .[2] IEA (International Energy Agency), (2009). World Energy Outlook 2009. Paris.[3] Witzeman, Metal bellow manual. 2010, Witzenmann GmbH.[4] Formosa, F.,A. Badel, and H. Favrelière, Development of low frequency, insulating thick diaphragmsfor power MEMS applications. Sensors and Actuators A: Physical, 2013. 189: p. 370-379.[5] Leissa, A.W. ( 1969) , Vibration of plates. NASA SP-160, Washington DC,

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Preliminary testing results of a diaphragm FPSE

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