From the early days of my first learning about Stirling engines, about 15 years ago, I've read the admonition not to use any lubricating oil on any Stirling engine. The problem with these engines (one of them anyway) is, no oil can ever be used, only dry lubricants, like graphite.
There are, I have just discovered through the site search, a few old threads on the subject of pressurization, I will be reading through, but none that I know of so far, address this specific issue in depth.
Recently, having purchased an engine that requires pressurization, I've been looking deeper into it and finding out some additional information I never knew, or never though about much before.
#1) As I've come to understand it now, the problem with pressurization and oil is, it turns the engine into a potential "bomb" because it can act like a diesel engine and the oil can spontaneously (or otherwise) ignite.
Well, one tidbit of information: - that can only happen at very high compression, like 2000 psi (?) (from the paintball video).
#2) High pressure air compressors, like my recent purchase: Yong Heng has the same problem. It can compress air to some 5000 psi + so why doesn't it explode?
Well, apparently it would, and so might any compressor, which is why compressors use a special compressor oil.
The question on my mind now is, why not just use compressor oil in a Stirling engine?
And, is this even an issue with Stirling engines that don't use high compression?
Is it really necessary that all small model Stirling engines use graphite pistons so they don't require oil and so don't explode?
It seems to me, while the danger is potentially very real, it may also have been overblown to some degree.
Pressurization & Lubricating oil
Re: Pressurization & Lubricating oil
I guess my main reason for asking is related to my fairly recent idea, or ambition to convert ordinary IC type small engines, like a 3 or 5 horse power Briggs and Stratton into a Ringbom type heat engine.
Something like this:
Would a little oil from the crankcase over on the right getting into the displacer chamber on the left constitute a fatal, potentially disastrous problem?
Supposing the entire thing we're pressurized in one way or another. Plug any ports, breathers exhaust/intake and fill it up with helium or whatever.
If an insert gas is used, such as helium, or any other kind of "shielding gas" used for mig welding, it seems to me that an "explosion" from the "diesel effect" or whatever would be literally impossible. The oil simply could not ignite or burn without oxygen.
On the "Jim Dandy" site, it is stated about that engine:
Using hydraulic fluid or compressor oil instead of regular motor oil would further mitigate any potential issue since, apparently, these do not have much issue with combusting even under extremely high pressure.
In this video the recommendation, near the start of the video, is to use, (for the Yong Heng compressor), a "diester" compressor oil.giving his recommendations of a few of the various brands available:
https://youtu.be/Rf2Df4ev7lE
OK, so at about $25 / qt. That's a little expensive, but how often would it need an oil change, with external combustion? No burnt fuel to contaminate it.
Something like this:
- Resize_20220820_110037_7146.jpg (135.62 KiB) Viewed 4257 times
Supposing the entire thing we're pressurized in one way or another. Plug any ports, breathers exhaust/intake and fill it up with helium or whatever.
If an insert gas is used, such as helium, or any other kind of "shielding gas" used for mig welding, it seems to me that an "explosion" from the "diesel effect" or whatever would be literally impossible. The oil simply could not ignite or burn without oxygen.
On the "Jim Dandy" site, it is stated about that engine:
I'm not entirely sure about the location of the "oil cups" in proximity to the displacer/firebox, but it seems this engine was in some way lubricated with plain old oil while also being pressurized to a moderate degree.Continuous Power Rating: 2.5Hp
Pressurization: Air, Helium, CO2 or Argon at up to 300psi
Burner: Wood fire box capable of natural convection of forced air draft
Lubrication: Periodically filled oil cups
Using hydraulic fluid or compressor oil instead of regular motor oil would further mitigate any potential issue since, apparently, these do not have much issue with combusting even under extremely high pressure.
In this video the recommendation, near the start of the video, is to use, (for the Yong Heng compressor), a "diester" compressor oil.giving his recommendations of a few of the various brands available:
https://youtu.be/Rf2Df4ev7lE
OK, so at about $25 / qt. That's a little expensive, but how often would it need an oil change, with external combustion? No burnt fuel to contaminate it.
Re: Pressurization & Lubricating oil
The Jim Dandy # 6 doesn’t have a crankcase, thus the simple oil cups like the old-timey engines. That’s the point of a double-acting Gamma — it can be pressurized without worrying about crank seals. It still has the piston and it’s rod seal, and the two displacer rod seals though, and I’ve no idea if they run dry or lubed. The Diesel effect isn’t caused by pressure, it’s caused by compression; 20 psi isn’t much, but compressing 1 psi suddenly to 20 would be hot enough for ignition. That ratio wouldn’t change whether you started at 1 psi or 100 psi. I’ve no idea what the “compression ratio/expansion ratio” of Jim Dandy # 6 is, but I wouldn’t expect it to be much over 2/1, so as to leave room for heat to get in from the low-tech chunk firewood burner without constant tending. Regardless of compression heat though, I would think that even just a red-hot heater could be problematic for regular lubes, whether from explosion or maybe just carbon buildup, so if there’s any potential contact I would certainly buy the special oil.
Bumpkin
Bumpkin
Re: Pressurization & Lubricating oil
OK, thanks.
I just thought all this time that the reason nearly all model Stirling engines on the market have graphite pistons, even little LTD engines, was to avoid the use of oil.
I don't particularly like graphite. It seems to be very fragile and tends to wear pretty quickly, but I assumed there was no real good alternative
Anyway, why would it matter if the oil is in a crankcase or a rod seal?
Here is one place I probably read a long time ago, but have come across such warnings again and again over the years, most of which did not go into as much detail
https://www.stirlingengine.com/buy/#12
I just thought all this time that the reason nearly all model Stirling engines on the market have graphite pistons, even little LTD engines, was to avoid the use of oil.
I don't particularly like graphite. It seems to be very fragile and tends to wear pretty quickly, but I assumed there was no real good alternative
Anyway, why would it matter if the oil is in a crankcase or a rod seal?
Here is one place I probably read a long time ago, but have come across such warnings again and again over the years, most of which did not go into as much detail
https://www.stirlingengine.com/buy/#12
It only takes a little bit of oil, leaking around a piston into the hot section to become the fuel source for an explosion
Re: Pressurization & Lubricating oil
I've wondered about this,..
I've been a small engine repair mechanic most of my life.
The worst thing that I know of, that can happen from getting some oil in the combustion chamber from warn rings, worn valve stems or whatever, is smoke in the exhaust, carbon build up, fouled spark plug.
In fact, it is common practice in diagnosing an engine to remove the plug and squirt some oil in the cylinder to see if that gets an engine started, as it helps seal up the gap in warn rings or bad valves of some other compression problem.
We are surrounded all day long by lawn mowers, chain saws, weed eaters, automobiles, ets. etc that ALL have SOME oil getting into the cylinders all day long. 2 cycle gas has the oil mixed in with the gas. Diesel engines RUN on, what is essentially a kind of oil.
Are we afraid, or is anyone worried about these various IC engines "exploding" though the oil/gas/fuel is being intentionally compressed and intentionally ignited under high compression?
So ... And all these engines have crankcases full of oil right there, just millimeters from, if not virtually in direct contact with the combustion chamber.
So... what about getting any minute quantity of oil anywhere near the power cylinder (or displacer chamber) of a Stirling engine is so much more dangerous?
Under what actual circumstance could a little oil transform a Stirling engine into a "BOMB" ?
I've been a small engine repair mechanic most of my life.
The worst thing that I know of, that can happen from getting some oil in the combustion chamber from warn rings, worn valve stems or whatever, is smoke in the exhaust, carbon build up, fouled spark plug.
In fact, it is common practice in diagnosing an engine to remove the plug and squirt some oil in the cylinder to see if that gets an engine started, as it helps seal up the gap in warn rings or bad valves of some other compression problem.
We are surrounded all day long by lawn mowers, chain saws, weed eaters, automobiles, ets. etc that ALL have SOME oil getting into the cylinders all day long. 2 cycle gas has the oil mixed in with the gas. Diesel engines RUN on, what is essentially a kind of oil.
Are we afraid, or is anyone worried about these various IC engines "exploding" though the oil/gas/fuel is being intentionally compressed and intentionally ignited under high compression?
So ... And all these engines have crankcases full of oil right there, just millimeters from, if not virtually in direct contact with the combustion chamber.
So... what about getting any minute quantity of oil anywhere near the power cylinder (or displacer chamber) of a Stirling engine is so much more dangerous?
Under what actual circumstance could a little oil transform a Stirling engine into a "BOMB" ?
Re: Pressurization & Lubricating oil
I’ve never seen a description of the Philips engine that caused their fatal accident, only that the event led to their using other gasses. I suspect the problem has to do with external combustion engine heat exchangers being made as thin as possible for efficiency, compared to more robust internal combustion engines not needing exchangers at all.
Bumpkin
Bumpkin
Re: Pressurization & Lubricating oil
I've searched for hours and can't really come up with anything definitive regarding the circumstances. Other than that this Phillips case is the one and only known such incident.Bumpkin wrote: ↑Mon Aug 22, 2022 10:05 am I’ve never seen a description of the Philips engine that caused their fatal accident, only that the event led to their using other gasses. I suspect the problem has to do with external combustion engine heat exchangers being made as thin as possible for efficiency, compared to more robust internal combustion engines not needing exchangers at all.
Bumpkin
Was this something that occured in the course of research at the Phillips research lab or in an actual production engine is not specified.
Also older "antique" Stirling engines were previously routinely pressurized with air, without incident.
In the course of my search, I came across this article (PDF):
https://citeseerx.ist.psu.edu/viewdoc/d ... 1&type=pdf
Some mention is made of the Philips explosion but the entire article is very interesting. It makes several references to the conversion of IC engines (diesel mostly) and air compressors into Stirling Ringbom engines.
Excerpt:
Free-displacer Ringbom-Stirling engines
One of the simplest mechanical arrangements is the so-
called free-displacer Stirling engine devised by Ossian
Ringbom in 1905 and shown diagrammatically in Fig. 3.
In this arrangement the displacer moves entirely under
the action of fluidic forces with no mechanical connec-
tion to the piston or crankshaft.
This arrangement is particularly attractive for conver-
sion of existing diesel engines or air compressors to
operate as Stirling engines because it provides the
potential for drastic reduction in the development cost
of new engines. A 20 kW demonstration Ringbom-
Stirling air engine with water lubrication is shown in
Fig. 4. This unit is based on the conversion of a Lister
8/1 diesel engine. Work is in progress on this engine at
the University of Calgary and is described in detail else-
where (5). An extensive treatment of Ringbom-Stirling
engine theory is given in (6).
Although a simple mechanical arrangement, the
Ringbom-Stirling engine is a complicated thermo-fluid
system controlled by a combination of variable mean
fluid pressure to regulate output and variable gas spring
volumes to regulate speed.
This concept of using the "gas spring" to regulate engine speed is something that occured to me as a possibility not long ago:
- Resize_20220823_000226_6816.jpg (140.21 KiB) Viewed 4202 times
Both the conversion as well as the regulation, except in this paper they are not talking about just small IC engines but locomotive engines.
- Resize_20220823_001325_5878.jpg (73.57 KiB) Viewed 4202 times
Re: Pressurization & Lubricating oil
As far as possible lubricating oil for any sort of pressurized Stirling engine, like a converted IC type engine with a crankcase, I'm not out of the woods yet, by just using hydraulic fluid or compressor oil...
Looking deeper into it, there are all kinds of such fluids/oils/lubricants, HUNDREDS actually, some synthetic, some water based and some petroleum based, many of which are quite flammable and potentially explosive under high pressure.
There are some rather exhaustive studies on the subject but so far, the ones I've come across have been behind a pay wall. (Judging only from titles and/or abstracts).
Probably the water based lubricants would be the safest, but which, name brands or formulations available on the market are actually water based ? And would they even work or be appropriate for use in a Stirling engine ?
I'm inclined to think at this point, absent some actual record of the circumstance, that the Philips accident probably occured in the course of research, trying to find the limits of how much air pressurization could be safely used, and upon finding out in a tragic way, switched to inert or alternative oxygen free gases so as to push the limit further.
It is, IMO unfortunate that practically nothing seems to be known for certain,
Accounts of this alleged explosion all seem to be second hand, years after the alleged event., Very brief, lacking any detail, where, when, who,... Specifications, pressures involved, if any, leading to a lot of FUD rather than progress.
Looking deeper into it, there are all kinds of such fluids/oils/lubricants, HUNDREDS actually, some synthetic, some water based and some petroleum based, many of which are quite flammable and potentially explosive under high pressure.
There are some rather exhaustive studies on the subject but so far, the ones I've come across have been behind a pay wall. (Judging only from titles and/or abstracts).
Probably the water based lubricants would be the safest, but which, name brands or formulations available on the market are actually water based ? And would they even work or be appropriate for use in a Stirling engine ?
I'm inclined to think at this point, absent some actual record of the circumstance, that the Philips accident probably occured in the course of research, trying to find the limits of how much air pressurization could be safely used, and upon finding out in a tragic way, switched to inert or alternative oxygen free gases so as to push the limit further.
It is, IMO unfortunate that practically nothing seems to be known for certain,
Accounts of this alleged explosion all seem to be second hand, years after the alleged event., Very brief, lacking any detail, where, when, who,... Specifications, pressures involved, if any, leading to a lot of FUD rather than progress.
Re: Pressurization & Lubricating oil
I thought this study should prove enlightening on the subject:
"System Safety in Stirling Engine Development"
https://ntrs.nasa.gov/api/citations/198 ... 016459.pdf
As I was reading through the document however, discussing all the seemingly endless potential areas for "catastrophic failure", I had to check the title, was this about Stirling engines or hydrogen fueled vehicles, carrying tanks of compressed hydrogen.
There seemed to be a great deal of emphasis focusing on things like high pressure hydrogen filled transfer lines under the car that could rupture, from being hit by rocks, valves, seals, pumps etc. that could come loose from vibration and storage tanks that could be propelled in a collission etc. all of which seemed to have nothing to do with the (my/our) area of interest: a hermetically sealed, pressurized Stirling engine.
Well, as it turned out, reading along, the engines being studied were supposed to be speed and/or power regulated by pressurization, and depressurization of the engine. Want to slow down? Depressurize the engine. Want to speed up? Pump more hydrogen into the engine. That is, by continually transferring hydrogen between hydrogen storage tanks and the engine, via high pressure pumps, through valves, transfer lines, all manner of connection points, fittings, elbows etc etc etc at 4500 psi ( 300 ATM).
IMO a completely preposterous proposition.
Of course there would be failures
Not with the engine itself, just all to the, IMO, completely rediculous and unnecessary storage and transfer apparatus.
If I did not know any better, I would to think these studies were intentionally contrived to discourage the use of Stirling engines,
"System Safety in Stirling Engine Development"
https://ntrs.nasa.gov/api/citations/198 ... 016459.pdf
As I was reading through the document however, discussing all the seemingly endless potential areas for "catastrophic failure", I had to check the title, was this about Stirling engines or hydrogen fueled vehicles, carrying tanks of compressed hydrogen.
There seemed to be a great deal of emphasis focusing on things like high pressure hydrogen filled transfer lines under the car that could rupture, from being hit by rocks, valves, seals, pumps etc. that could come loose from vibration and storage tanks that could be propelled in a collission etc. all of which seemed to have nothing to do with the (my/our) area of interest: a hermetically sealed, pressurized Stirling engine.
Well, as it turned out, reading along, the engines being studied were supposed to be speed and/or power regulated by pressurization, and depressurization of the engine. Want to slow down? Depressurize the engine. Want to speed up? Pump more hydrogen into the engine. That is, by continually transferring hydrogen between hydrogen storage tanks and the engine, via high pressure pumps, through valves, transfer lines, all manner of connection points, fittings, elbows etc etc etc at 4500 psi ( 300 ATM).
IMO a completely preposterous proposition.
Of course there would be failures
- Resize_20220825_055357_7077.jpg (82.29 KiB) Viewed 4162 times
If I did not know any better, I would to think these studies were intentionally contrived to discourage the use of Stirling engines,
Re: Pressurization & Lubricating oil
I've actually been wondering, ever since seeing the Infinia engine, why it has this gigantic fill valve jutting out, practically begging to get broken off. I was even more surprised after removing it and seeing how small and short the threaded end was.
I would have thought that if the fill valve could not be entirely eliminated, for the obvious reason that there must be some means of filling the engine with working fluid, it should at least be as unobtrusive as possible. Preferably, completely recessed and the recess capped off with a plug, that could be completely and permanently sealed.
Having this big valve jutting out of the engine where it could fairly easily be broken off, just seems like somebody asking for trouble.
Having one fill valve that could break off or fail, or be tampered with, at 500psi jutting out is bad enough,
Having some enormous high compression pump, lines running all over the place, tanks and all that at over 4000 psi on a moving vehicle, is just insane.
I would have thought that if the fill valve could not be entirely eliminated, for the obvious reason that there must be some means of filling the engine with working fluid, it should at least be as unobtrusive as possible. Preferably, completely recessed and the recess capped off with a plug, that could be completely and permanently sealed.
Having this big valve jutting out of the engine where it could fairly easily be broken off, just seems like somebody asking for trouble.
- Resize_20220825_073851_1499.jpg (55.01 KiB) Viewed 4160 times
Having some enormous high compression pump, lines running all over the place, tanks and all that at over 4000 psi on a moving vehicle, is just insane.
Re: Pressurization & Lubricating oil
An interesting video demonstrating the advantages of helium & pressurization.
https://youtu.be/9oZw4rX8kPg
Though, I think that his theory about WHY it works is probably wrong
Both Helium and Hydrogen, have unusually high thermal conductivity for gasses.
A Stirling engine is ultimately driven by the "hot" high energy gas molecules colliding with the piston.
Pressurization simply puts more gas molecules into a smaller package making more collisions in a shorter time frame possible.
https://youtu.be/9oZw4rX8kPg
Though, I think that his theory about WHY it works is probably wrong
Both Helium and Hydrogen, have unusually high thermal conductivity for gasses.
A Stirling engine is ultimately driven by the "hot" high energy gas molecules colliding with the piston.
Pressurization simply puts more gas molecules into a smaller package making more collisions in a shorter time frame possible.
Re: Pressurization & Lubricating oil
I've been torture testing various lubricants with the propane torch.
Looking for something inert, nonflammable, that theoretically might be used in the crankcase of a Stirling engine, in order to avoid any possibility of "dieseling" or explosion.
https://youtu.be/8HGqud8gj0g
Surprisingly, two of the special lubricants highly recommended for use in high compression compressors that I had assumed would not be flammable turned out to be no better than ordinary cooking oil.
Silicone spray, which I had high hopes for was, I think, worst of all.
Machinist cutting oil, surprisingly was not that great.
Probably the sewing machine oil was second place after vegetable oil.
I've heard, or known for a long time that vegetable oil could be used to run a diesel engine, so things are not turning out too well so far.
The best candidate so far, is already known to explode under pressure in a diesel engine.
I'm still looking to source some water based lubricants to try, so I'm not giving up yet.
If I do find something that is non-flammable, or apparently so, the next step, I guess, would be to test the flammability or explosiveness under high pressure.
That could get a little dangerous. I'm not sure of a safe way to go about it, or any way, for that matter.
Atomize the oil/lubricant under high pressure and then try to ignite it and see if it can explode.
Maybe a soda bottle, or other container that can be pressurized, with a schrader valve and a spark plug tapped into the side.
Looking for something inert, nonflammable, that theoretically might be used in the crankcase of a Stirling engine, in order to avoid any possibility of "dieseling" or explosion.
https://youtu.be/8HGqud8gj0g
Surprisingly, two of the special lubricants highly recommended for use in high compression compressors that I had assumed would not be flammable turned out to be no better than ordinary cooking oil.
Silicone spray, which I had high hopes for was, I think, worst of all.
Machinist cutting oil, surprisingly was not that great.
Probably the sewing machine oil was second place after vegetable oil.
I've heard, or known for a long time that vegetable oil could be used to run a diesel engine, so things are not turning out too well so far.
The best candidate so far, is already known to explode under pressure in a diesel engine.
I'm still looking to source some water based lubricants to try, so I'm not giving up yet.
If I do find something that is non-flammable, or apparently so, the next step, I guess, would be to test the flammability or explosiveness under high pressure.
That could get a little dangerous. I'm not sure of a safe way to go about it, or any way, for that matter.
Atomize the oil/lubricant under high pressure and then try to ignite it and see if it can explode.
Maybe a soda bottle, or other container that can be pressurized, with a schrader valve and a spark plug tapped into the side.
Re: Pressurization & Lubricating oil
Maybe getting somewhere:
https://youtu.be/uKUk8vSl7yg
Tentatively speaking, but I need to look into it more.
I think, from a brief scan over search result titles and previous reading, phosphate ester oils are, (I think) used in association with air conditioning systems. (And possibly gas turbines ? Need to do more research)
(BTW it was someone at a local hardware store who mentioned "turbine oil" when I enquired about nonflammable lubricants, that set me down this avenue.)
AC is another area where there is a potential for dieseling/explosion from high pressure gas situations. See this article for example:
https://hvacrschool.com/the-dangers-of- ... explosion/
https://youtu.be/uKUk8vSl7yg
Tentatively speaking, but I need to look into it more.
I think, from a brief scan over search result titles and previous reading, phosphate ester oils are, (I think) used in association with air conditioning systems. (And possibly gas turbines ? Need to do more research)
(BTW it was someone at a local hardware store who mentioned "turbine oil" when I enquired about nonflammable lubricants, that set me down this avenue.)
AC is another area where there is a potential for dieseling/explosion from high pressure gas situations. See this article for example:
https://hvacrschool.com/the-dangers-of- ... explosion/
Re: Pressurization & Lubricating oil
Some interesting information presented in this video regarding Stirling engine lubrication problems and solutions.
I'm not too surprised about the silicone lubricant apparently burning up and gumming up the seals and , clogging up the regenerator (possibly?) After seeing how it is quite flammable at very high heat in my own tests.
He does a 1hour run of the engine dry, (no liquid lubricant) with only PTFE seals in a subsequent video. This apparently worked quite well.
https://youtu.be/GBuv5-5B2OI
The liquefaction of some gasses was first achieved using burnt leather seals.
I'm not too surprised about the silicone lubricant apparently burning up and gumming up the seals and , clogging up the regenerator (possibly?) After seeing how it is quite flammable at very high heat in my own tests.
He does a 1hour run of the engine dry, (no liquid lubricant) with only PTFE seals in a subsequent video. This apparently worked quite well.
https://youtu.be/GBuv5-5B2OI
The liquefaction of some gasses was first achieved using burnt leather seals.
Re: Pressurization & Lubricating oil
I recently came across a paper which stated:
A little over 200 psi.
I tend to believe that is accurate for a number of reasons.
The Infinia executive in an interview bragged about how their solar engine DID NOT require high pressure. Though he did say "about 500 psi" as I recall.
Secondly, the fill valve on the engine, and/or the available couplers that are able to fit it, are generally not the sort of high pressure fitting I would have expected.
Senft, in his books that cover Stirling engine pressurization states and graphically illustrates with numerous diagrams how pressurization is only useful to a point, after which it actually becomes detrimental, or less and less advantageous.
The conductivity of a gas is determined by its "mean free path" or something or other, so the denser it becomes, the less heat it is able to conduct. As pressurization increases density, the value of high pressurization in a Stirling engine seems rather dubious and a kind of trade off at best
So modest pressurization can increase the molecular density so more energy can be delivered to the piston, up to a point, after which, the gas molecules become more and more "crowded" making heat/energy transfer through or by the gas, through the engine more and more difficult.
Otherwise, could the 1.6 MPa for the 3 kw engine be a misprint or something? I don't think so.
Also, "mean pressure" suggests that the initial charge might actually be lower. Since, I would have to assume that heating the engine to some 800° F or more would increase the average pressure considerably.
The cooling water, presumably, would not go below the ambient filling temperature. So logically the "mean pressure" could not fall below the initial charge, but could run higher than the initial cold fill pressure.
https://www.mdpi.com/1996-1073/14/21/7009/pdf...the engine could reach
an efficiency of 28% with 1.6 MPa of mean pressure
A little over 200 psi.
I tend to believe that is accurate for a number of reasons.
The Infinia executive in an interview bragged about how their solar engine DID NOT require high pressure. Though he did say "about 500 psi" as I recall.
Secondly, the fill valve on the engine, and/or the available couplers that are able to fit it, are generally not the sort of high pressure fitting I would have expected.
Senft, in his books that cover Stirling engine pressurization states and graphically illustrates with numerous diagrams how pressurization is only useful to a point, after which it actually becomes detrimental, or less and less advantageous.
The conductivity of a gas is determined by its "mean free path" or something or other, so the denser it becomes, the less heat it is able to conduct. As pressurization increases density, the value of high pressurization in a Stirling engine seems rather dubious and a kind of trade off at best
So modest pressurization can increase the molecular density so more energy can be delivered to the piston, up to a point, after which, the gas molecules become more and more "crowded" making heat/energy transfer through or by the gas, through the engine more and more difficult.
Otherwise, could the 1.6 MPa for the 3 kw engine be a misprint or something? I don't think so.
Also, "mean pressure" suggests that the initial charge might actually be lower. Since, I would have to assume that heating the engine to some 800° F or more would increase the average pressure considerably.
The cooling water, presumably, would not go below the ambient filling temperature. So logically the "mean pressure" could not fall below the initial charge, but could run higher than the initial cold fill pressure.