By: Peter Lynn, March 2021
Stirling cycle engines operate on a closed cycle in which a quantity of gas (called the working fluid), is alternatively heated and cooled. Mechanical power is generated by the heated gas expanding against a piston. It is then moved to a cool space and contracts before being returned through the heater to repeat the cycle. Gas control is entirely by volume changes, not by valves. The traditional working fluid is air, but nitrogen is sometimes used because it's less corrosive. For high performance, helium and hydrogen are better because their thermal conductivity is much higher- and hydrogen is also less viscous. For high specific outputs (power for size), the working fluid is pressurised- sometimes to more than 100bar.
Engines with Stirling-like features were built from around 1800 (including by airplane pioneer Sir George Cayley in 1807), but their invention is generally credited to the Rev. Robert Stirling, after whom they are named. Stirling, a Scottish Presbyterian minister, developed the first practical valveless closed cycle engine and patented the regenerative heat exchanger (a key feature) in 1816.
Heat is applied externally to Stirling cycle engines (like for steam engines), rather than internally (as for the diesel or petrol engine and most gas turbines). They can therefore use the combustion of any solid, liquid, or gaseous fuel- or a high temperature source such as solar, nuclear, or geothermal.
In 1840, French scientist Sadi Carnot described the second law of thermodynamics, which sets a limit (the Carnot cycle) for heat engine efficiency that cannot be exceeded no matter how perfectly an engine is designed or constructed. It is a function only of the maximum and minimum temperatures, the formula being: (Th - Tc)/Th. Engines using the Carnot cycle have not yet proven to be practicable. Rudolf Diesel mistakenly thought that he could achieve this and caused much embarrassment to himself and his licensees by claims to this effect made in his patent. Stirling engines (and their open cycle Ericsson cousins) are the only heat engines that are theoretically capable of Carnot efficiency. They do this indirectly by using heat exchangers to store heat energy remaining in the working fluid after expansion and returning it after the cooling stage. Stirling engines operating on a cycle reasonably similar to the theoretical Stirling cycle can be built.
During the 19th century, Stirling cycle air engines (often called hot air engines) were relatively common, especially for water pumping, but also for sewing machines, dentist drills, and domestic fans. Unlike steam engines, they did not require boilers, but low power and high cost limited their uses. An 8" Ericsson Stirling engine (1870's to 1930's), weighs 350kgm, developed 200watts (1/4hp)- and cost more than a year's average NZ income back then. Production of Stirling cycle air engines tapered off in the early 20th century as electricity reticulation spread and inexpensive internal combustion engines became generally available.
Driven by the multi-fuel options of the Stirling cycle and its high potential efficiency, there were many attempts at reviving the Stirling engine during the 20th century. Some were aimed at mainstream applications such as cars, but Stirling engines were also tried for submarines, solar electricity generation, artificial hearts, and combined heat and power (CHP) units- in which small Stirling engines generate electricity for household use with waste heat being applied to water heating (Whispergens for example).
The reality after 200 years of striving by countless engineers and huge expenditure (more than NZ$100million for Whispertech I believe), is that Stirling engines have yet to find any long-term mainstream market except for toys, a shrinking niche in cooling (the Stirling cycle can be used in reverse for cooling- in thermal imaging for example) and for submarines (combustion can be at very high pressure- and they're quieter than nukes). Combined heat and power units are currently not economic for general use, even with "green" subsidies. Nor, after a brief flurry, have CHPs secured a place in the off-grid or recreational boating markets. Various solar Stirling energy park projects have foundered as the cost of photovoltaics has come down.
Why is this? The essential problem is that their theoretical efficiency has so far proven to be unattainable without exceeding a price that makes the engines impracticable. Even very expensive designs using hydrogen or helium working fluid pressurised to more than 100 atmospheres are typically less than 25% efficient and have low specific output (power for size). They compare unfavourably with compact petrol engines that approach 30% efficiency, diesels with more than 40%, solid-state photovoltaics, and now solid-state refrigerators.
The Whispergen saga, in which I had a small part, raised quite a few questions of the type that are interesting to me and that I am now able to pursue without time, money or management constraints. Whispertech began in my workshop in 1987 when Don Clucas, who had worked for me while at school and for a few years full time, returned to start his engineering PhD developing a Stirling engine based combined heat and power unit. After Southpower came in as a sponsor, development moved to Christchurch, and my direct involvement ceased (by the early 1990's kite traction- my real job- was really taking off). The Whispergen design soon settled on a 4 cylinder 'alpha' layout- in the main because of its perfect balance and heat transfer scale effects which favour small cylinder sizes. Don had also invented the wobble-yoke crank system for it, which gave the embryonic company what the backers felt was essential IP. This was undoubtedly the best approach from a business perspective but leapfrogged many engineering options and left some questions unanswered. Since 2008, I have been indulging myself by looking into some of these with a series of one-off engines: LSM 11 to 18, with 19 under construction (2021). I don't have any expectation of commercial opportunities or even of finding anything that the world will find useful, it's all for fun and to satisfy my curiosity.
There are three main Stirling engine layouts: alpha, beta and gamma.
Alphas use two single acting cylinders connected via a heater, regenerator and cooler, with the pistons around 90 degrees out of phase to shuttle the working fluid back and forth. Four cylinder alphas have every cylinder leading the following one by 90 degrees, with the top of each connected to the underneath of the next. They have only one main seal per cylinder which minimises seal friction.
Betas have a single acting piston and a double acting displacer in the same cylinder also at around 90 degrees phasing.
Gammas use a double acting displacer in one cylinder and a single acting piston in a second cylinder, also at around 90 degrees phase.
Additionally, there are free piston Stirling engines which are beta layout. Their piston and displacer motions are controlled by spring, gas pressure, inertia, and solenoid. A hybrid form called Ringboms use crank controlled pistons with their displacer moved by spring, weight, inertia and gas pressure.
LSM's 11, 12, 13, 14, 15 and 18 are betas, 17 and 19 are alphas
To make comparisons easier, all of them have swept volumes of around 2.5litres, use air as the working fluid and are unpressurised. I chose this larger size mainly so that the engines would have enough power to be actually useful. LSM 14 is in a boat- which does 5knots with 3 people aboard. LSM 12 is in a motorbike- which is slow but ridable- and bounces up and down a lot. Larger sizes are also easier to make with ageing eyesight.
I don't build them as an exercise in model engineering- the engineering is a means to an end, not an end in itself (my excuse for rough and ready construction!).
They use conventional piston rings- mainly because these are much more resistant to occasional temperature spikes and have a lot less friction than Teflon based dry seals. Surprisingly, oil residue build-up has not been a problem so far- though CI rings do preclude extended use of mesh regenerators. LSM 14, in an 8m replica 19th century great lakes gentleman's launch, has run for 100's of hours and does not yet require de-carbonising.
Not pressurising the working fluid is partly to make the engines more visually accessible but also because 'atmospherics' are a style that has been neglected since the 19th century except for toy engines- most would say for very good reason considering their low specific power! So called 'snifter' one-way valves can be used to boost pressure in the working space a little, but I have met very few air engines ever (especially antique ones) that don't run better with the snifter off, because the pumping losses from the snifter exceed the gains from higher density working fluid. Sealing has to be exceptionally good for snifters to be useful.
I also confess to two other foibles: using found materials and 'designing as I build'- no drawings.
There's a scrap yard next door to my 'Engineerium' from which I scrounge all the steel pipe, stainless steel, disc brakes (for rings), bolts, and 'recycled' bearings required. This is not because of honourable necessity but because I'm a curmudgeonly miser. I haven't yet found a free source for argon or inserted tips for tooling.
The "no drawings" approach is a sort of intellectual challenge- like chess I suppose. Can I think out the entire design in advance and hold it in my head well enough not to have any bits inconveniently trying to occupy the same space when it's time to put everything together? The order in which parts are made makes this a lot easier, and I do record some dimensions at time- and have some failures, which I don't much talk about.
Another handicap is lack of facility with CAD, and CFD (computational fluid dynamics)- which is rather embarrassing, seeing as in 1968 I was possibly one of the first NZ engineers to be able to play with an embryonic program in this field- "IBM Stress". A 1980's reverse Polish notation Hewlett Packhard calculator still gets daily use and I do have a Stirling engine modelling program into which I can plug numbers. I have never yet had useful predictions from this - an experience that parallels Dr Don's (Whispertech, now a Uni lecturer) who also has a rather low opinion of their usefulness. My two engineer sons have only contempt for these inadequacies- one of them a CFD specialist, having been with Team NZ in a previous AC challenge.
Lockdown provided a solid period of interruption-free workshop time during which I built LSM 16 and 17, and rebuilt 15 completely with different linkages, displacer, hot end, burner and tank. New materials (stainless steel especially), improved fabrication techniques (like TIG welding), rolling element bearings and better understanding of thermodynamics have informed significant performance gains for unpressurised hot air engines. Specific output (power/swept volume) of the LSM series is around twice the 19th century averages. They are also much more compact (which has more to do with this being a particular focus of mine rather than anything inherent) and are MUCH lighter. LSM 14 (in the boat) has the same swept volume and more power than the 8" Ericsson pumping engine in the earlier photo.
An early theme was to make an engine that could power a boat using driftwood, and later, by burning books- my brother-in-law disposes of tonnes of them in his work with Ashburton's yearly Bookarama. There was also a cheeky idea to burn religious tracts- which can arrive at your door free of charge, given even the slightest encouragement.
LSM 11 was therefore made for solid fuel, though I soon found out that higher class literature has too much clay in the paper for clean burning, while Mills and Boons are excellent (and conveniently sized). 11 has tube heat exchangers which necessarily require that the displacer has seals. For unpressurised air engines, this extra friction limits the available nett output- to around 200watts in this case. LSM12, 13 and 14 therefore used annular surface heat exchangers and contactless displacers- though, being a slow learner, I did go back to a displacer seal for 15-1, just to remind myself of the friction cost- and lubrication difficulty.
With engines 12 to 16, I've explored optimal heat transfer areas:
If too little, revs and hence power is limited. If too large, gas flow losses rise and extra dead space reduces volume changes, which also limits output. Alpha layouts have higher intrinsic 'compression ratio' so are much less sensitive to this than betas. Around 1,200 sq.cm of cold end heat transfer area and 1000 sq.cm for the hot end has so far proven optimal for this range of engines.
I also settled on gas flow cross section during this time. There's a dead volume cost in having this too large, pumping losses if it's too small, and smaller cross sections provide better heat transfer by turbulent flow- a complex balance. Between 11sq.cm and 15sq.cm works well, though I have often ended up with a larger cross section than desirable for mechanical reasons:
Which are the difficulties of keeping the gap between the displacer and the hot end cylinder to under 3mm (which is already 20 sq.cm for a 200mm bore) solely by sliding elements that are more than 500mm distant. It's easy to do in the workshop when the engine is cold, but with the hot end at more than 700 degrees,
temperature asymmetries in the burner and even wind effects, dreaded scraping noises are never far away, especially after a few hundred hours running. Nothing spoils a pleasant cruise on the lake as much as crunching sounds and the accompanying drop in boat speed. LSM 12, 13, 14, 15 and 17 have different displacer guide systems, all of which are satisfactory, but as yet no clear favourite has emerged.
LSM 13 is a conventional Beta but is fully balanced by virtue of double geared cranks and has an extreme bore/stroke ratio (320mm bore, 32mm stroke). The idea behind this is that main seal frictional losses for reciprocating engines is in an inverse relationship with bore- the larger the bore the less friction losses for the same swept volume. Unfortunately, the leakage path also increases with bore and for 13, I haven't been able to get good enough sealing without using ring 'spring' which would add more friction than I was expecting to save. The gear trains are also noisy.
By 2016 I had some ideas as to the key parameters and had tried all manner of good ideas that weren't. LSM 12 and 17 started life as open Ericsson cycle engines- now usually called the Brayton or gas turbine cycle- which I failed to get running.
LSM 12 in this early manifestation didn't even express a preference for rotational direction (what I call Jude 1 on the Stirling engine power scale- St Jude being the patron saint of lost causes- and love affairs.
LSM 16 has is a quite different layout, not alpha, beta or gamma, but with a combined piston/displacer that changes length while reciprocating. It runs OK but, predictably, has difficulties with the main seal- which is internal to the piston/displacer and hence not easy to cool. I call it an Adiabatic layout as the power taken by repeatedly compressing the piston/displacer's internal volume is largely recovered adiabatically.
LSM 18 is, at last, a serious (and possibly successful) attack on what I have regarded as one of the main failings of Stirling engines since Whispergen days. To explain this, I first have to describe how heat transfer in Stirling engines actually works. The theoretical cycle is for the working fluid to emerge from the regenerator at its maximum (or minimum) temperature and then have heat added (or removed) as expansion (or compression) occurs so as to maintain the working fluid at constant temperature during this part of the cycle (the essential characteristic of Stirling cycles). In practice, working fluid passes from the regenerator into a heater (or cooler) and then into the expansion (or compression) space where it expands (or contracts) with a significant temperature drop (or rise).
In both alpha and beta engines, more than 50% of the expansion (which is what generates the power) happens after the working fluid has begun to pass back through the heater, regenerator and cooler into the cold space. The best way to understand this is to look at the wooden models I use- yes, yes, I will get a nice dynamic Solid Works depiction of this organised someday. I'm not that sure what effect this has on efficiency, though it must be negative because the working fluid is being cooled even as it's expanding against the piston to do useful work, but it will certainly reduce output significantly. Gamma layouts are at least as bad in this respect- they generate power via a piston which is in the cold space and responds to general variations in the working fluid pressure. The gamma layout is however very suitable for low temperature difference engines, and for toys and models that only have to overcome their own friction.
This working fluid transfer problem is entirely a function of the mechanical arrangement. Free piston and Ringbom engines could be arranged so as to avoid it, but don't ever seem to be. For free piston engines this is most likely because of the limitations imposed by how displacer and piston motions are controlled (various complex harmonics). I've shied away from delving into this because it looks like several lifetimes work. For Ringboms, the classic 19th century layout provides far from ideal working fluid transfer and the hours I've spent attempting to figure out improvements using magnets, springs and gas seals have not yielded much progress so far.
LSM 15-4 uses a star linkage that improves working fluid transfer somewhat relative to conventional betas.
LSM 18 uses a modified Whitworth quick return motion that is a substantial solution to the transfer problem- at some cost in additional element loads.
Are these engines actually better and by how much? They seem to be a step forward, but I don't know for sure yet- and won't until I can get them into a state to take maximum loads- and get my new dynamometer operating, having cannibalised its predecessor for another project.
15-4 currently has a steel piston/steel bore which tends to pick-up when I put it under load at max revs.
18 isn't yet sealing very well and has some clonks which will require better hardening of the curved quick return track, and maybe a larger diameter roller also, as this is subject to around 3 times the load of the scotch yokes that work so well in the other betas of this series. I may also have to make a lighter displacer for it- which is not a small job.
The other main failing of current Stirling engines that I've been trying to figure out a practical way to attack for years is the inherent inefficiency in passing the working fluid back through the heater (cooler) after expansion (compression). Theoretically the working fluid is already at max (min) temp as it re-enters the heater (cooler) but in practice there is a significant temperature drop (rise) during expansion (compression). An effect of this is that the working fluid then enters the regenerator at higher (lower) temperature than it would otherwise be, which requires the regenerator to be larger than necessary. This imposes extra gas flow losses and more dead space. There are also unnecessary extra gas flow losses in the heat exchangers themselves.
LSM 18, a type of alpha, is an attempt to solve this. It's to use mechanical slide valves to route the working fluid directly from the expansion and compression spaces to the regenerator, bypassing unnecessary extra passes through the heater and cooler. This could be done with pressure operated automatic (non-return) valves, but I've settled on mechanical operation for now so as to reduce pressure losses and be able to fiddle with timing. Although the hot end valve must function at up to 500 degrees, it can be non-contact as even 90% efficacy will be enough. I had earlier been trying to work the valving into a beta but couldn't find a practical arrangement- and had concerns about excessive dead space, which betas are more sensitive to. For years I've also been trying to figure a way to accomplish this goal by using swirl- keeping the working fluid rotating around the piston and displacer axis so as to give it preference for a port that short circuits the heater (cooler)- but haven't been that confident of my attempts to calculate the effects (and I'm not able to peer in there to see what is actually happening). In the longer term, swirl may be the best solution- but first I need to find out whether the expected benefits materialise.
Peter Lynn, Ashburton, New Zealand, March '21
- Jude 1: No discernible preference for rotational direction.
- Jude 2: Clear rotational direction preference but not self-sustaining.
- Jude 3: Almost self-sustaining; tantalisingly close to.
- Jude 4: Occasionally self-sustaining, but sometimes stops spontaneously.
- Jude 5: Mostly self-sustaining- almost never stops spontaneously.
- Jude 6: Easily self-sustaining- with excess enough to run its cooling fan.
- Jude 7: Some power: Could spin the "Lotto" wheel (for small numbers).
- Jude 8: Useful power; like from half an unfit person on an exercise machine.
- Jude 9: Really useful output; enough to power a mobility scooter (but not uphill).
- Jude 10: Power commensurate with cost and complexity (Never achieved yet).