THERMODYNAMICS Revista Mexicana de Fısica S59 (1) 199–203 FEBRUARY 2013

Developing and testing low cost LTD Stirling engines

G. Aragon-Gonzalez∗, M. Cano-Blanco, A. Canales-Palma, and A. Leon-GaliciaPDPA, Universidad Autonoma Metropolitana-Azcapotzalco,

Av. San Pablo # 180. Col. Reynosa. Azcapotzalco, 02200, D.F.Telefono y FAX: (55) 5318-9057.∗e-mail: gag@correo.azc.uam.mx

Received 30 de junio de 2011; accepted 25 de agosto de 2011

The construction of miniature LTD Stirling engine prototypes, developed with low-cost materials and simple technologies is described. Theprotypes follow the Ringbom motor array, without mechanical linkages to actuate the displacer piston. Different designs, sizes, materials andmechanisms components have been tested. The power piston has been replaced with a flexible diaphragm and the mechanisms linkages wereconstructed with piano steel wire. Power output and efficiency experimental measurements are presented for two miniature LTD Stirlingengines, the MM7 model fromAmerican Stirling Companyand our simplest low cost model. A reasonable design to build low cost engines,rendering brake power and thermal efficiencies about 40 % those obtained with similar commercial engines, but only 5 % the cost has beenobtained.

Keywords: Stirling cycle; LTD machines; Ringbom motors; power and thermal efficiency measurement.

Se describe la construccion de prototipos de maquinas Stirling LTD miniatura, desarrollados con materiales de bajo costo y tecnologıassencillas. Se apegan al modelo de motor Ringbom, sin eslabones mecanicos para actuar el piston de desplazamiento. Se han sometido aprueba diferentes disenos, tamanos, materiales y componentes para los mecanismos. El piston de potencia se remplazo con un diafragmaflexible y los eslabones de los mecanismos se construyeron con alambre cuerda de piano. Se presentan mediciones experimentales de lapotencia y la eficiencia para dos maquinas Stirling LTD miniatura, el modelo MM7 deAmerican Stirling Companyy del mas sencillo denuestros modelos de bajo costo. Se obtuvo un buen diseno para construir maquinas de bajo costo, que entrega 40 % de potencia y eficienciatermica desarrollada por modelos comerciales semejantes, pero con solo 5% del costo.

Descriptores: Ciclo Stirling; maquinas LTD; motores Ringbom; medicion de potencia y eficiencia termica.

PACS: 01.50.Kw; 01.50.Pa; 07.10.Pz; 07.20.Pe

1. Introduction

The operation of several thermal machines, devices designedto convert internal energy in mechanical work, is well de-scribed using the thermodynamic power cycle concept. Oneof these engines is the Stirling motor, a device that follows afour times closed regenerative cycle operating with an idealgas as the working substance

The main subject of Robert Stirling’s original design wasa heat exchanger, called originally “economiser” for its en-hancement of fuel economy to run the engine. The heat ex-changer takes up a part of the energy of hot gas leaving theexpansion chamber to deliver it when the cold gas goes backto the chamber. Now it is generally known as ’regenerator’.

The ideal gas undergoes successive expansions and com-pressions, due to the heat exchanging from hot and cold tem-perature sources. The ideal Stirling cycle consists of fourthermodynamic processes (Fig. 1 below): 3-4, the gas is ex-ternally heated and undergoes an isothermal expansion; 4-1,the gas transfers heat to the regenerator and follows an iso-choric cooling process; 1-2, the gas undergoes an isothermalcompression, transferring with the cool temperature source;2-3, the compressed gas receives heat from the regeneratorand follows an isochoric process [1].

A Stirling engine is not an internal combustion engine; itreceives the heat from any external high temperature source.

For example the waste heat rejected to the environment fromseveral industrial or manufacturing processes.

FIGURE 1. Ideal regenerative Stirling cycle.

200 G. ARAGON-GONZALEZ, M. CANO-BLANCO, A. CANALES-PALMA, AND A. LEON-GALICIA

FIGURE 2. Gamma engine with separate cylinders.

The net work output W (J) for the ideal cycle is, [2]:

W = mR lnV1

V2(TH − TC) (1)

where m (kg) is the mass of the gas enclosed by the engine, R(J/kgK) is the specific gas constant, V1 (m3) is the enclosedgas volume with the power piston at highest position in itscylinder, V2 (m3) is the gas volume with the power piston atlowest point, TH (K) is the temperature of the engine hot-sideand TC (K) is the temperature of the engine cold-side.

2. Power production on a Stirling engine

The thermal efficiency of any Stirling engine is defined as theratio of the power output to the heat transferred from the hightemperature source. Schmidt developed a model to predictthe power output of a Stirling machine, [3-5]; the workingsubstance is treated as an ideal gas and the compression andexpansion as isothermal processes.

The gas changes of volume in any Stirling engine aresynchronized with the cyclic piston stroke, from the upperto the lower dead point; they can be expressed with a sinu-soidal function. The theoretical predictions from the Schmidtmodel approach to the behaviour observed in real engines, forany of the mechanical Stirling engines configurations. Thesemechanical configurations are generally divided into threegroups known asα, β andγ arrangements.

Alpha engines have two pistons in separate cylinderswhich are connected in series by a heater, regenerator andcooler. Both Beta and Gamma engines use displacer-pistonarrangements, the Beta engine having both the displacer andthe piston in an in-line cylinder system, whilst the Gammaengine uses separate cylinders (Fig. 2)

From the initial Schmidt analysis several other authorshave proposed mathematical models for Stirling engine ther-modynamic analysis. Chen and Giffin [6] identified 25 dif-ferent models. Beale proposed an empirical equation to cal-culate the power output of the Stirling engine, by:

Bn =w

pmVpf(2)

where pm is the medium cycle pressure (bar), Vp the powerpiston stroke (m3), f the cycle frecuency (Hz). This dimen-sionless parameter Bn is called Beale number [7]. Typicalvalues for the Beale number are 0.11 to 0.15 when consider-ing high temperature differential engines [8].

3. Low temperature difference Stirling en-gines

In 1982 Kolin developed a Stirling engine to produce me-chanical work from a temperature source lower than the boil-ing water [9]. In 1992 James R. Senft received a request fromthe National Aeronautics and Space Administration (NASA)to build a Stirling engine operating with a very low tem-perature difference (LTD motors). Senft built the N-92 en-gine [10]; this Stirling engine runs with∆T as low as 6◦Cand even with the heat produced with a warm hand on a coldday

Several researchers are developing new LTD Stirling en-gines [11-13], to fit them to some low temperature differenceor use several sources of waste heat. The Mexico City sub-way company has recently expressed his interest to build anduse 1 (kW) Stirling engines. The purpose is to make use ofthe heat generated in the electric train systems or obtainedfrom solar collectors, to provide electric power for the light-ing system in the train stations. Even though the initial fi-nancing may be expensive, this request may be satisfied withLTD Stirling

FIGURE 3. Ringbom miniature engine (Carl Aero Co.).

Rev. Mex. Fis. S59 (1) (2013) 199–203

DEVELOPING AND TESTING LOW COST LTD STIRLING ENGINES 201

FIGURE 4. MM7 LTD engine pointing downwards in the testingfacility. A Dynamometer; B Voltmeter; C Electric multimeter; DSwitch; E Variable voltage transformer; F Adiabatic recipient; GDigital thermometer; H Fan; I LTD engine; J Optical tachometer;K Weight.

motors; for example extending the Gaynor et al design for a500 (W) prototype [2].

Senft [14] has improved his designs and built RingbomGamma type engines, running with∆T of only 0.5◦C TheRingbom Stirling engines have no mechanical linkage to ac-tuate the displacer piston. Pressure changes inside the enginecaused by the movement of the power piston act on an over-sized displacer pushrod to create movement of the displacerpiston.

Miniature LTD Ringbomγ engines develop power in theorder of 1 to 10 (mW), shaft torques below 3×10−4 (Nm),angular speeds under 500 (rpm) with thermal efficiencies be-low 0.1% (Fig. 3). They are built sometimes as scientifictoys, but can be employed with didactic purposes and to ex-plore the limits of useful low temperature difference. It is alsopossible to measure its power output and thermal efficiency,using simple methods and common instruments available inalmost any engineering school [15].

Equation (2) cannot be used to calculate the power outputof LTD Ringbom Stirling engines. Walker [16] proposed anempirical equation for these engines, with BN in function ofthe cold to hot engine temperatures ratio,τ = TC /TH :

BN = 0.034− 0.052τ (3)

Kongtragool [17] proposed the modified Beale number:

MBn =w

pm Vp f

[(1 + τ)(1− τ)

](4)

Typical MBN values for LTD engines are 0.25 to 0.35.

4. Testing LTD Ringbom engines

There are not any other means to know the thermal efficiencyand real power output from any thermal engine, but perform-ing measurements from primary variables. A testing facilitywas built to measure LTD Ringbom miniature engine perfor-mance [15].

The very low power figures (no more than 10 mW), madecompulsory to adapt typical testing designs to measure brakepower and heat transferred from the high temperature source,without using expensive laboratory instruments (Fig. 4).

The testing procedure consists of supplying the heat QH

(W) by electric means, measuring voltage and electric cur-rent (QH = ∆V i). An increasing torque M is applied to thepulley on the flywheel shaft, until permanent state is achievedwith shaft constant speedω (thenw= Mω).

FIGURE 5. Brake power (mW) vs shaft speed (rpm) and tempera-ture difference (◦C). MM-7 LTD engine.

Rev. Mex. Fis. S59 (1) (2013) 199–203

202 G. ARAGON-GONZALEZ, M. CANO-BLANCO, A. CANALES-PALMA, AND A. LEON-GALICIA

FIGURE 6. Efficiency (%) vs shaft speed (rpm) and temperaturedifference (◦C). MM-7 LTD engine.

FIGURE 7. Testing procedure with the MM7 LTD engine fromAmerican Stirling Company.

Brake power outputw (mW) and thermal efficiencyηe = w/qH are shown in Figs. 5 and 6, as functions of shaftspeed (rpm) and temperature difference (∆T = TH - TC ; ◦C),for the MM-7 LTD engine built byAmerican Stirling Com-pany(Fig. 7).

5. Low cost LTD Ringbom Stirling engines

Commercial LTD miniature engines like those shown inFigs. 3 and 7, may be very expensive due to the manufactur-

FIGURE 8. Small cost LTD ringbom engines.

FIGURE 9. Brake power (mW) vs shaft speed (rpm) and tempera-ture difference (◦C). Low cost LTD engine.

ing processes required to construct them; not only to achievetight geometrical tolerances but to get a shining ornamentalappearance.

Usually miniature Ringbom LTD engines have a smallamount of components, but besides the manufacturing costssome of them are constructed with expensive materials(borosilicate glass and aluminium-clad graphite for the powercylinder and piston, for example).

We have developed and tested several low cost miniatureRingbom LTD prototypes (Fig. 8). Different designs, sizes,materials and mechanisms components have been tested forits construction. Artisan processes and short-lasting materialshave been avoided, alike expensive materials.

The power piston has been replaced with a flexible di-aphragm and the power cylinder adapted from a small plasticrecipient. The displacer cylinder is manufactured with cop-per sheet with plastic glued walls. The flywheel is a compactdisc and the mechanisms linkages were constructed with pi-ano steel wire.

These low cost engines may operate with temperature dif-ferences∆T = TH -TC from 20 to 80◦C. The smaller one inFig. 8 has only 0.36 the heat transfer surfaces of the MM7 en-gine in Fig. 7. A discarded steel vessel works like displacer

Rev. Mex. Fis. S59 (1) (2013) 199–203

DEVELOPING AND TESTING LOW COST LTD STIRLING ENGINES 203

FIGURE 10. Efficiency (%) vs shaft speed (rpm) and temperaturedifference (◦C). Low cost LTD engine.

cylinder and the engine lacks of any refinement (like screwedunions, bearings for the gyratory axes or machined parts).

This extremely simple engine was tested in the facilityshown in Fig. 4, developing brake power and thermal effi-ciencies about 10% those obtained with the commercial en-gines MM7 (with similar temperature differences applied toboth engines, Figs. 9 and 10).

6. Conclusions

It seems very difficult to build any other device as inexpensiveand simple as the Stirling Ringbom LTD, in order to producemechanical work from a heat source. Nevertheless they show

the full attributes of thermal engines and admit a thoroughtesting.

Miniature Ringbom LTD engines have really small effi-ciencies, but allow making good use of very low tempera-ture waste heat sources (fully unsuitable for other thermalengines). Senft [14] proved the possibility to run continu-ously an engine with a temperature difference of only 0.5◦C,but ∆T of about 40◦C is a good practical limit to producemechanical power (for example using solar energy or wasteheat from air conditioning systems).

Commercial Ringbom LTD engines have elevated costs,highly related with its ornamental toy quality. These enginesmay be successfully simplified, even to extremely plain de-signs and yet showing smooth running with regular speed.We took these simplifications to the limit only for didacticpurposes. Now we have a reasonable design to build minia-ture Ringbom LTD engines, rendering brake power and ther-mal efficiencies about 40 % those obtained with similar com-mercial engines (but 5 % the cost).

The design of a Stirling engine to produce 1 (kW), usingwaste heat from a low temperature source, may be resolvedwith the Ringbom Gamma array. This motor has no mechan-ical linkages to actuate the displacer piston; the power outputwould be achieved with several displacer cylinders and powerpistons linked to a common flywheel shaft

To continue this work with a theoretical approach, itwould be convenient comparing the miniature LTD effi-ciencies with a model like the Novikov-Chambadal-Curzon-Ahlborn one, as it was made for the Otto cycle in Ref. 18.

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3. G. Schmidt,Theorie der Lehmannschen calorischen maschine(1871)151-12.

4. K. Hirata,Schmidt theory for Stirling engines. (National Mar-itime Research Institute. Japan. 1997).

5. J. Machacek, Analysis of Stirling engine characteristics bySchmidt’s theory.(Dept. of Electrical Power Engineering, Doc-toral degree programme. Brno, Czech Republic)

6. N. C. J. Chen and F. P. Griffin,A review of Stirling engine math-ematical models. (Oak Ridge National Laboratory. US Depart-ment of Energy 1983).

7. C. D. West,Theoretical basis for the Beale number, (Proceed-ings of the 16th Intersociety Energy Conversion EngineeringConference. Atlanta: American Society of Mechanical Engi-neers; 1981). [Paper 819787].

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15. M. F. Roberto, Caracterizacion de maquinas Stirling tipodesplazamiento. Bachelor’s thesis. (Universidad AutonomaMetropolitana, Unidad Azcapotzalco, Mexico, 2008). (in Span-ish).

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