Pictorial Steps To Make A Sterling Engine

Fig. 4.1. Cyclic temperature variation of the working fluid in the expansion and compression spaces of a Stii line engine operating with ndiabatic conditions in the two spaces (after

Lee 1976).

pre diet engine performance to one or two per cent of test-bed performance. In this regard it is interesting to observe that Percival (1974) wrote:

'In I9(>0 il was concludcd that there was slill too much deviation between actual and predicted engine performance particularly for I lie 59 kW (SO hp) cylinder size. The real engine always rejected more heal and produced less power than the analytical engine.'

No doubt substantial improvements have taken place in the subsequent decade ami there is no reason to doubt the claims made in several publications by workers at Philips of the ability to predict very closely the performance of actual engines.

Various straws in the wind gathered by the author over the years have led to the understanding that a family of computer programs has been developed by Philips. The various programs are thought to include some overall cycle-simulation programs foi the complete engine at various levels of sophistication and complexity whereas others are available for the detailed simulation and design of single components or subassemblies in the engine, i.e. heater tubes, coolers, crank mechanisms etc.

So far as can be interpreted, the basis of the Philips thermodynamic-analysis simulation program is closely similar to that developed by

One of the main strengths of the Philips company is that close adherence over many years to similar design configurations has permitted the accumulation of extensive practical experience. On the basis of this, experience, 'fudge' factors of the proper magnitude can he judiciously applied to the analytical results to provide close and realistic simulation.

Indirect confirmation of Philips use of the adiabatic cycle with supplementary corrections was provided by Feurcr (1973) of MAN/MWM, a Philips licensee, in his splendidly illuminating discussion of the effect of phase angle («) on the power output anil efficiency of a Stirling engine.

Feurcr selected his engine parameters as representative of a single-cylinder Stirling engine built by MAN/MWM where 'measurements and calculations were largely in agreement.' The principal parameters for the example were:

Working gas Helium

Speed 1500 rpm

Cooler temperature (inside) 75 °C (167 °F) Heater temperature (inside) 750 °C (1382 °F) Carnot efficiency 66 per cent

Heater volume 100 cm5 (6.1 in3)

Regenerator volume 145.3cm1 (8.87 in')

Piston diameter 100 mm (3.9 in)

Connecting rod length 100 mm (3.9 in)

Variable parameters:

Phase a nglc 0- n rad (0-180 degrees)

Dead volume 0,40, 100, 200 cm3 (0,, 12.2 in3)

Diameter of connecting duct 100, 50, 20 mm (3.9, 1.97, 0.79 in).

He first calculated the power output and efficiency as a function of phase angle for the Schmidt cycle having the above design conditions and obtained the results reproduced in Figs. 4.2 and 4.3. These results refer to the case with zero dead volume, but in his paper F'eurer gave results for nine other cases with different dead volumes. Also included in these figures were the results calculated for the adiabatic cycle.

Feurer then corrected the resulls for the adiabatic cycle to include the 'adiabatic residual losses', described as follows:

'When lhe semi-adinbatic machine was calculated, ii was assumed that the temperature curve differed from the ideal temperature curve, but it was also assumed that I his difference was in phase with the pressure corve, as in the case of the ideal processes. This difference—(lie influence on the pressure amplitude has already been allowed for—also has an influence on the phase displacement

Phase angle a

Fto. •!2.. Power output of a Stirling engine as a function of vaiiation in the phase anjjlc a

(after Fcurer 1973).

temperature in lliis volume clement would result in a different mass, i.e. the deviating temperature curve wotikl produce a different mass distribution in the cycic and tins would result in a difTercnl pressure distribution. As compared with the old, ideal pressure distribution, this new pressure distribution has shifted by a certain amount. Thus, the following applies:

A difference between the ideal temperature in the cylinders, heat exchangers and connection spaccs on the one hand, and the actual temperature in these components on the other inevitably results in n phase displacement between pressure and volume.

These losses, which are called 'adiabatic residual losses', are probably at their maximum when the largest pressure amplitudes occur on account of the phase displacement.

At a large phase angle of the volumes, i.e when the volume between the pistons is only moved to and fro by the pistons and the pressure amplitude is only produced by the difference in temperature between the hot side and the cold side, tltis influence becomes negligible.'

The magnitude of the adiabatic residual loss is shown on big. 4.2. Its elTeci is shown on both bigs. 4.2 and 4.3 as the difference between the curves for the adiabatic cycle and that including the adiabatic residual loss.

A further correction was introduced to allow fot the aerodynamic-How loss resulting from the transfer of fluid about the engine. The magnitude flf llu1 acrn/Uinflmir-flmu Incc lo olc<i i-liiHim In Pin A T Willi •«-» .l..o.l

Includes adiabntic residual loss

Includes flow loss

Includes thermal conductivity loss

8IJ 6U 90 120 150 180

Phase angle a

.Schmidt cyulc

No (lend volume

Adiahatic cycle

FtO. 1.3. 'Ilicrmal cfficlcncy of a Stirling engine as a function of variation in phase angle "

fnfter Fcnrer 1973).

volume the flow loss was rather small as shown on Fig. 4.2 but was greater for the other cases considered by Feurer. Maximum volumes of the flow loss occurred at high values of the phase angle where the greatest mass flow rates of gas were involved.

Finally thermal losses by conduction were included. These had no ellect on the engine power output and only a relatively minor effect on the efficiency as shown by Fig. 4.3.

The above is an abbreviated, inadequate, summary of the very important paper by Feurer. published simultaneously with another of equivalent significance (Zacharias 1973). Those responsible for the publication of these papers ate warmly commended for their refreshing candour in presenting such fascinating material.

Hearsay has it, and tJie conference papers published in 1978 indicate, that a change in management policy at Philips will result in the future publication of material having greater significance than in the past. If trtie the trend is to be encouraged for they have been remarkably coy. revealing no more than the momentary 'flash of an ankle.'. The current heavy research investment of public funds in the U.S. will demand 'full fromal exposure1 and will, no doubt, flush out an interesting item or two nooa1. analysis

Nodal analysis of Stirling engines was pioneered by Finkelstcin 11975a) but later, several other nodal analysis programs were prepared independently.

In nodal analysis programs the attempt was made to model the simultaneous energy and fluid Hows occurring in the engine and thus simulate exactly the engine cycle and performance. This was achieved by writing and resolving equations for the conservation of mass, momentum and energy for particular nodes, cells or elements of the engine. The equations were too complex for general analytical solution and, thus, were solved numerically in terms of small incremental time steps. Hie equations were invariably reduced to one-dimensional form with additional simplifications introduced depending on the author.

A complete and comparative discussion of the various programs developed and available is beyond the scope of interest of this book (as well as beyond the competence of this author). Readers are therefore urged to consult the source documents referenced in the following notes.

All the nodal analysis programs are basically similar in their general approach. The design of engine to be simulated must be known in exact detail to the extent that the mechanical arrangement, cylinder-wall thickness and material, heat exchanger tube diameter, fin dimensions or matrix pore sizes arc all specified. This design is then broken down, as experience dictates, into a number of nodes elements or control volumes. Some operating conditions must be specified such as charge pressure, and temperature of the energy source and sink.

Differential equations for the conservation of mass, momentum, and energy must be developed and generally converted to difference equations. Iimpirical formulae for the aerodynamic-friction and heat-transfer effects must be included, and an equation of slate for the working fluid. A mathematically stable method must then be found for numerical solution of the difference equations to resolve the pressure, temperature, and mass distribution in the engine at the end of a particular time step, given the conditions at the beginning of the step.

The usual procedure for solution is to start with some initial arbitrary assumed conditions anil then proceed through several engine cycles until quasi-steady state is achieved, that is when the instantaneous cyclic values of pressure, temperature, and mass distribution are not significantly different from the preceding cycle.

Finally the cyclic pressures and volumes are integrated to calculate work transfers. Heat flows are estimated and the overall thermal efficiency computed.

In most cases an isothermal Schmidt cycle-type calculation is included

Flo. •L'L Three-dimensional representation of Ihc fcns temperature versus node position and cyclic angle in a Stirling engine (after Schock 1978b).

The results arc presented in a variety of formats. Typically the input data in terms of engine geometry and operating parameters is restated foi comparison purposes. This is followed by tabulations at selected cyclic crank intervals of pressures, temperatures, velocities, mass content, and mass velocities at representative stations in the engine. Finally considerations of the overall cycle are presented, usually in terms of energy flows, work terms, heat transferred, or ratios of these such as the thermal efficiency.

Most programs now incorporate automatic plot routines so that, if required, the data can be presented pictorially as well as. or even instead of being tabulated. Some remarkable three-dimensional pictures can be produced in this way. Figs. 4.4 and 4.5 were given by Schock (1978a) and arc typical of the interesting and informative representations achieved by computer automatic plot routines. These particular diagrams show the variation in temperature with node position or volume as a function of the evelie anple.

I IG. -15. Three-dimensional representation of the gas temperatures versus node volumes nnd cyclic angle in a Stirling engine (niter Scliock l'>78aj.

Hnkelstein nodal analysis Following the important development of the adiabatic analysis discussed above, Theodor Finkelstein continued working on increasingly sophisticated theoretical aspects of Stirling engines. This effort culminated during the late 1960s in the adaptation of the NASA Thermal Analysis Program (T.A.P.) to Stirling-cycle simulation and the creation of what is believed to be the first nodal analysis program.

The first practical application of the simulation program was at the University of Calgary in 1968/69 in support of the development of miniature cryogenic cooling engines for the British Ministry of Technology. Pig. 4.6 shows- a simplified cross-section through the cooling engine. Fig. 4.7 shows the two-dimensional representation of the engine used for ilie nodal analysis simulation. This work was briefly discussed by Finkelstein, Walker, and Joshi (1971). Following some further refinement and development, Finkelstein (1975a) presented Ihc theoretical basis for the analysis and described the numeric differencing technique for solution of

Philips Stirling Engine Cooler

Fig. 4.6. Simplified cross-section of small Stirling-cycle cryogenic cooling engine. A— regenerator, B—compression space, C— piston, D—expansion space, B—cooler. !■'■—

displace! rod.

Fig. 4.6. Simplified cross-section of small Stirling-cycle cryogenic cooling engine. A— regenerator, B—compression space, C— piston, D—expansion space, B—cooler. !■'■—

displace! rod.

The Piukelslein nodal analysis program is now installed on a commercial computer network and available for general use on payment of a royalty fee. Potential users may obtain further details from Dr. T. Finkclslcin, TCA Inc., P.O. Hox 643, Beverley Hills, Ca.

b'ricli nodal analysis Israel Urieli. a mature graduate student working under the supervision of Professor C. Rallis at the University of Witwatersrand, has provided the most complete and comprehensive discussion (Urieli 1977) of Stirling-engine simulation by nodal analysis. His thesis is required reading for all those professionally interested in the field of Stirling-engine computer simulation. A good outline of the approach, and one more readily available than copies of the thesis, was provided by Urieli. Rallis,

Cryogenic Stirling Engine

Ftpanslon spacc^



75 Gai nodes-

Matrix mulct




< ^impression Space I


I'rewurniit Q-

l;m. 4.7. Two-dimensional representation of the nod.nl analysis network for the small cryogenic cooling engine shown in Fig. 4.6.

The thesis contains a complete program listing in Fortran language of the complete Uricli program. The program is likely to be applicable to engines of a configuration other than the model assumed for investigation by Uricli. However experience with other computer programs suggests that very substantial effort would likely be required to establish a fully operational version of the Uricli program.

It is understood that work in the nodal analysis field continues at the University of Witwatersrand under the direction of Professor Rallis. Activity includes experimental work to validate the computer model and the investigation of alternative theoretical models (Berchowitz, Rallis, and Uricli 1977).

Martini (1978a) states that the Uricli thesis contains three errors in the main program and that corrections may be obtained from I. Uricli. Ormat Turbines, P.O. Box 68, Yavnc, Israel.

Up-to-date information about his work on Stirling engines may be obtained on application to Professor C. Rallis, Department of Mechanical Engineering, University of Witwatersrand. South Africa.

Simpower nodal analysis program

Gcdeon (197N) has outlined the techniques of Stirling-engine simulation in use at Sunpower of Athens, Ohio, manufacturers of the Ik-ale free-piston Stirling engines. Numerical simulation is an integral part of development at Sunpower. Engine refinement and program validation proceed hand-in-hand with routine daily exchanges between the staff engaged in laboratory and theoretical work.

It is understood that the Sunpower program is fast and fully validated. It is, in reality, a complex of programs capable of cycle simulation at different levels of sophistication as selected by the program controller. 1'he program is self optimizing to the degree and according to criteria specified in the program input.

There is no doubt that in the field of Stirling engines, Sunpower has accumulated the greatest body of practical engine development and operating experience, supported by computer simulation, outside of Philips and their licensees. It is therefore gratifying to note that the Sunpower simulation programs are available for general use on a contract basis. Furthermore, active moves arc afoot (Beale 19781) to install the program on a commercial computer network and to organize 'schools' for education in the use of the programs. Further details of this and other aspects of Sunpower Stirling engine development may be gained from William Bcale. President. Sunpower Inc., Athens, Ohio.

Schock. nodal analysis program

Schock (1978a) has described the Stirling Nodal Analysis Program (SNAP) prepared by Fairchild Industries under contract to the U.S. Department of Energy in support of a Beale free-piston Stirling engine developed by Mechanical Technology Inc. and Sunpower Inc.

The Schock program appears to be closely similar in many respects to the Urieli program described above and developed simultaneously. It is well described in the draft report (Schock 1978a) referenced above and presumably intended for general distribution as a U.S. Department of Energy Contractor Report. An abbreviated description may be found in the paper (Schock 1978b) listed in the literature for the 1978 Intersociety Energy Conversion Engineering Conference.

It is expected that the program may be validated with reference to the performance of the free-piston engine described by Goldwater and Morrow (1977). Furthermore it is possible the program could be installed and made available for general use on a commercial computer network.

Details of the status of the program may be obtained from Alfred Schock. Energy Systems Department, Fairchild Space and Electronics Co., Germantown. Maryland.

I.ewis Research Center nodal analysis program

Roy Tew and others I lew 1978) at the NASA Lewis Research Center. Cleveland. Ohio, have developed a Stirling-engine nodal analysis program as part of the total DOE/NASA Stirling Engine Automotive Program. The description of the Lewis program given by Martini (1978) suggests that il may he less rigorous than the Schock or Urieli programs referenced above.

Simultaneously with the theoretical work, experimental studies are being carried out al the Lewis Research Center (Cairelli et al. 1977). It is thought to be likely that in the long run, the final answer to computer simulation and experimental validation will be placed in the public domain by the team at NASA Lewis Research Center. Readers are therefore urged to consult the current literature relating to the DOE/NASA Stirling Automotive Engine.

Further details may be obtained on application to Robert Ragsdalc, Stirling Engine Project Office, NASA Lewis Research Center, 21000 Brookpart Road. Cleveland. Ohio.

i'inegold/Vanderbrug nodal analysis program }

Finegold and Vanderbrug (1977) have outlined a nodal analysis program foi Stirling-engine simulation developed at the .let Propulsion for underwater applications. Present status and potential applications of the computer program are not known.

Organ nodal analysis program

Or Allen Organ formerly of King's College, University of London, now with the School of Engineering, University of Cambridge, has published a series of recent papers indicative of a powerful nodal analysis type program in formation, if not yet fully developed. Readers are advised to consult recent contributions or contact Dr. Organ directly for an up-to-date appreciation or the status of development.

Philips/United Stirling/MAN/MWM nodal analysis programs

Several papers have hinted at the existence and use of nodal analysis type programs at Philips and their licensees. No details have been given. It is understood that for general design work, adiabatic-cycle programs arc preferred over the more sophisticated nodal analysis programs.


Stirling-engine simulation by nodal analysis is an expensive, time-consuming activity to be reserved for those professionally engaged in Stirling engine development ami application, or for those academics engaged in the training and education of engineers at the graduate level.

At the present time no comprehensive comparison or evaluation is available of the various Stirling-engine simulation programs described above. Martini (T97Sa) has attempted the preparation of a design manual including a comparison of the various theoretical procedures. However he has unfortunately concentrated his efforts principally on isothermal type analyses with only passing reference to the more sophisticated nodal analyses.

Therefore at this time Stirling engine analysis is largely a horse-race where 'you pays yer money and yer takes yer choice'.

In terms of nodal analysis, the programs by Urieli and Finegold/Vandcrbrug arc completely listed in the references cited above. However neither of these programs has been extensively validated by reference to experimental data. Similarly the programs by Schock and by Tew arc neither listed in the references cited and have yet to be extensively validated experimentally. Furthermore, at the time of writing neither program is installed and available commercially.

Finkelstein's program is available commercially on payment of moderate royalties but no adequate documentation of validity with reference to practical engines is available.

Finally, the Sun power program is available commercially and has been validated extensively during the development of Bcale-typc free-piston —1 anni;#»nhiiiiv of the program to engines with crank mechati-

thought to present no particular problem, for it is generally reckoned in the trade that, from the aspect of simulation, free pistons are more difficult to handle than disciplined pistons.

Therefore, at this lime, for those wishing to obtain a computer simulation or optimization of a Stirling engine concept (1978) the program of choice has to be the Sunpower version followed by Finkelslcin model. The situation is extremely fluid and could change profoundly in a short time. One possibility is that Philips or Ihcit licensees could offer consultancy services to evaluate new concepts using theii undoubted expertise and experience in the field. Various straws in the wind suggest this may be more likely a prospect than previously so that enquiries of this nature to North American Philips. United Stirling, or General Electric may well be appropriate.

Whatever the model selected il is certain that the few companies and individuals wishing to operate at the highest levels of Stirling engine simulation and optimization must be prepared to invesl several weeks and considerable funds to establish the. program procedure and to accomplish the work.

Por those unable to alford the luxuries of nodal analysis a close study of the excellent manual by Martini (1978a) is recommended. The validity of his enthusiasm for so-called 'second order design' methods is not yet well established. Users of the manual arc therefore cautioned to be discriminating. Of particulai concern is Martini's view that an isothermal analysis corrected for various thermal and fluid effects can he an adequate basis for design.

The visceral feeling of this author is that the adiabatic cycle with the proper thet ino/lluid corrections can be appropriate for most serious work in the design and optimization ol Stirling engines. The adiabatic cycle does require the use of digital computers but not to an unconscionable degree and these are now so readily available that their use may be considered routine by most engineers. The adiabatic cycle, while a long way from actual conditions, is a good deal better than the isothermal case and requires only minor computing cost and time compared with nodal analysis. Readers sharing this view are therefore referred to the thesis by Lee (1976) and to the works of Rios, Qvale and Smith referenced below.

At yet an earlier stage in design isothermal analyses may be adequate. Martini (1978a) has developed techniques suitable for analysis using the small pocket calculators.

Finally at the start ol a project it is usually sufficient to carry out a simple Schmidt cycle calculation using the equations given above. To attain the likely performance of a practical engine one simply divides the efficiency anil power output by two (if one is an optimist) or by three (if one is a realist).

Solar Stirling Engine Basics Explained

Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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