Modified "Hot" Beta engine

[stephenz]

All dimensions (diameter and strokes) being equal, Alpha's have the highest compression ratios simply due to having 2 pistons rather than a piston and displacer.

Remember that for a beta and gamma the compression ratio is this: r =Vmax/Vmin = Vtot / [Vtot - Vswp] where Vtot is the total engine volume and Vswp is the swept volume of the power piston.

Beta's only have a small advantage over Gamma in the fact they tend to have less dead volume (no transfer tube needed), as such, everything else being equal Vtot is smaller for a Beta than a Gamma, if you analyze the equation above this yields a slightly larger compression ratio. I say slightly because it's generally good practice to minimize dead volumes (regardless of working with a Beta and Gamma).


With an Alpha configuration, since you have 2 pistons, the equation above is much more complex since the advance angle (typically 90degrees) has a different impact on the total volume. Again, if everything else is equal (stroke, piston diameters), the Alpha will always win in compression because it will necessarily have a much smaller Vmin compared to a Beta and Gamma configurations.


For a hobbyist grade, high power, high temperature engine you will find compression ratios in the range of 2+ for an Alpha, and 1.2-1.6 for a similarly sized Gamma or Beta engine... Again these numbers are for high power / high efficiency / (i.e. high temperature) engines. Compression ratio is really NOT the name of the game even at the highest hobbyist levels, especially if you're looking at an LTD. Hobbyist usually prefer looking at the ratio of swept volumes which are in my opinion and experience at the core of the best rules of thumb you should follow if you want to be successful building an engine, especially a high temperature one.

Of course, if you really want to have the highest compression possible on a beta or gamma, you can "cheat" by reducing the volume of the displacer compared to that of the power piston, but good luck if you're going that, as you can only go so far before the temperature requirements become ridiculous. Engines piston swept volumes larger by 20-25% than the displacer swept volume (beta/gamma with compression ratio in the range of 1.8-1.9) will require very, very high temperatures to run. According to Allan Organ's books, these have the among the highest efficiency and power but are also the most difficult to engine due to the ridiculously high temperature required.

One last thing, if you plan on building a high temperature engine with DIY tools, you would probably want to have a Displacer swept volume of roughly 50% greater than that of the power piston. This translates into a compression ratio of roughly 1.3:1 at best.


Asides from the basic geometric considerations and fundamental differences between an Alpha and a Beta/Gamma, why are these numbers what they are you might ask? They are mostly the product of numerical analysis (mostly iterative computation) based on hard sciences - i.e. equations (thermodynamics, heat transfer, fluid mechanics for the most part). And it turns out, these numerical analysis are backed up by prototype testing, i.e. actual testing confirming the analysis. Stirling engines are poorly adopted for a large number of reasons, but the fact is they are well understood. No magic.

[Tom Booth]

All dimensions (diameter and strokes) being equal, Alpha's have the highest compression ratios simply due to having 2 pistons rather than a piston and displacer.
...

I wouldn't say that, necessarily. Not without changing the crank offset in some way, if that's possible to do and still have a running engine.

The compression ratio in a conventional Alpha is relatively low, in spite of having two pistons because when one piston goes up (compression) the other goes down (expansion)

I've slowed down this animation:

ezgif.com-speed.gif (279.09 KiB) Viewed 4496 times

Also I want to compress HOT gas or add heat to the gas as near as possible just before full compression. In an Alpha, heat is added mostly during expansion or at constant volume (one piston going up while the other goes down) so, simultaneous compression and heating does not happen. There is really hardly true compression at all in an Alpha, like I say, unless the crank offset were modified.

I think, due to the difficulty of rapidly transferring heat into an external combustion engine, the compression ratio should ideally, be somewhat higher than a typical IC engine.

[Tom Booth]

I opened this thread with the rather bold statement that:

My reasoning and experiments over the years has led me to believe, right or wrong, that heat engines don't require cooling. At this point I no longer feel that this is just theorizing, I think I've demonstrated experimentally that it is at least possible, and in my estimation, a Stirling type heat engine often runs better without any kind of cooling jacket or sink.

Logically, to my mind anyway, a heat engine runs on heat so why should it ever be intentionally cooled? OK, Yes I know, Carnot limit and all that, the further the heat "falls" down to cold the better. So, the objective is to cool the heat engine down to absolute zero, or at least get it down as cold as possible, then heat it back up as hot as possible etc. etc.

Sounds good in theory I suppose, but is it actually true? Does it really work in practice?

Anyway, conjecture aside, I've been pondering what sort of design could be used to eliminate the cold side...

A few minutes ago I was reading through the comments on a model Stirling engine phone charger video. Someone commented that one of HIS Stirling engines could be used to MELT his phone.

Curious, I clicked over to his channel and saw that he has a number of DIY, home built Stirling engine videos on his channel.

Among them I found this one:


https://youtu.be/u-YfPEFBh70?si=BhpcibAgO---u9F_


Now, what is rather curious is that, if I understood him right, he said that "evidently" his engine likes to have the cooling water at over 200 degrees. I assume Fahrenheit, near boiling, so he has these copper coils wrapped around the flue pipe of his wood stove to pre-heat the cooling water.

Well, OK. so he is not educated about how Stirling engines run on a temperature differential and the cooling water should be as cold as possible to increase the temperature difference and he should really not be pre-heating the cooling water but should instead put ice in the pool.

But apparently, not knowing any better he found by simple trial and error that the engine actually ran better and with more power if the circulating cooling water was boiling hot instead of cold.

Of course we should all ignore that because, well, it simply can't be true. RIGHT???

Well, no, I think that maybe it is actually true.

I've been saying for a while now, not only does a Stirling engine not require cooling AT ALL, but if it is actually operating as I suspect, and is acting as a heat pump drawing heat from the cold side and transferring the heat over to the hot side, cooling the cold side might only have limited usefulness because the engine actually needs to be able to draw some heat from the cold side.

So you have two heat sources, one hot and one VERY hot, or one hot and the other less hot, but really, on an absolute temperature scale, ambient air is actually quite hot, about 300 Kelvin. A long way from 0 K.

Anyway, I left a comment asking for some clarification about the pre-heating of the cooling water. Maybe he is using hot water as the heat source?

After reading his description though, he says because the engine seems to like the cooling water so hot, he could just use air cooling and simplify the engine quite a bit as it apparently doesn't need water cooling, but likes to run hot.

Somebody should call the 2nd law police on this guy, I think he might be in violation somehow.

[Tom Booth]

I just had the thought that the engine might run better with hot water on the colder side of the engine, rather than air, because water can transfer heat very rapidly but air is an insulator.

So, if the engine is drawing a portion of its energy from the colder (or less hot) side, like a heat pump, then the hot water would supply a steady source of heat at a suitable temperature rather than being a source of cooling.

Air "cooling" might not supply sufficient heat as air is not as good a conductor of heat as water.

I don't yet know how his transition over to air cooling turned out, but I'll try and find out. I suspect it may not have been good, but not for the reason that might be supposed; that water cools better.

Water also heats better.

[stephenz]

I wouldn't say that, necessarily. Not without changing the crank offset in some way, if that's possible to do and still have a running engine.

The compression ratio in a conventional Alpha is relatively low, in spite of having two pistons because when one piston goes up (compression) the other

Have you even read the rest of the response? There are a few paragraphs with pointers proving this to you. All things being equal (yes that includes the same 90 degrees phase angle), Alpha's have greater compression ratio than Beta/Gamma's. That's all I am responding to, to help you, with something you can easily verify yourself mathematically with high school level trig.

I won't engage in responding to the non-sense of engines running better without cooling, I've tried before and it was useless you neither have the scientific intuition needed nor the heat transfer background needed.

[Tom Booth]

I wouldn't say that, necessarily. Not without changing the crank offset in some way, if that's possible to do and still have a running engine.

The compression ratio in a conventional Alpha is relatively low, in spite of having two pistons because when one piston goes up (compression) the other

Have you even read the rest of the response? There are a few paragraphs with pointers proving this to you. All things being equal (yes that includes the same 90 degrees phase angle), Alpha's have greater compression ratio than Beta/Gamma's. That's all I am responding to, to help you, with something you can easily verify yourself mathematically with high school level trig.

I won't engage in responding to the non-sense of engines running better without cooling, I've tried before and it was useless you neither have the scientific intuition needed nor the heat transfer background needed.

Well, thank you stephenz, I do very much appreciate your being here and I do appreciate the input.

Yes, I did read the rest of your response. I read through it very thoroughly, several times and gave it a great deal of serious thought and careful consideration. I do, or did intend on reading through it again and possibly commenting on it paragraph by paragraph.

However, at this point, just being honest, I don't see how the rest of your post has any bearing on the opening paragraph about Alphas having the highest compression ratio "simply due to having 2 pistons".

There are additional factors involved besides mathematics.

For example, if I have a water pump with a high flow rate (gallons per minute) but have it rigged up to pump water out of and back into the same water source the net gpm is zero.

In an Alpha, one piston is very often going up while the other is going down. One compressing while the other is expanding the gas, so the effective compression can be seen by direct observation and common sense analysis to not be as high as it might be if both pistons were compressing the gas simultaneously, which could be accomplished by changing the crank angle. That would however, involve machining a new crankshaft and ignoring the whole theory upon which the Alpha and Stirling engines in general are supposed to be based.

I say "supposed to be" because after figuring out the linkage in Robert Stirling's original design as laid out in the 1816 patent there is no displacer piston offset or advance. Both displacer and power piston approach TDC simultaneously so that the "cold space" at the back or underside of the displacer at TDC is fully occupied by the power piston, effectively eliminating the cold space "dead volume" which allows a higher effective compression ratio.

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So, no disrespect stephenz but I stand by what I can clearly see and determine myself through my own research and direct observation. So far, notwithstanding your barrage of insults, I haven't found your "pointers" or mathematical proofs, such as you've presented so far, particularly persuasive. But I will reread your entire post again. In the mean time feel free to continue making your argument or demonstrating some proof, mathematic or otherwise, that you can have any real compression during an isochoric process.

It might be educational to actually build a scale model of the 1816 engine, I think it is rather fascinating and I'm not sure if it's ever been done. I've never seen a working model anyway.

[Tom Booth]

Remember that for a beta and gamma the compression ratio is this: r =Vmax/Vmin = Vtot / [Vtot - Vswp] where Vtot is the total engine volume and Vswp is the swept volume of the power piston.

(...)

With an Alpha configuration, since you have 2 pistons, the equation above is much more complex since the advance angle (typically 90degrees) has a different impact on the total volume. Again, if everything else is equal (stroke, piston diameters), the Alpha will always win in compression because it will necessarily have a much smaller Vmin compared to a Beta and Gamma configurations.

(...)

The above passages appear to be the extent of your statements regarding the mathematics associated with the Alpha which amounts to no more than saying it's "more complex".

Vmax/Vmin is not the least bit complicated.

If you simply add the two cylinder volumes together

Vmax1+Vmax2/Vmin1+Vmin2 the results are bound to be misleading due to the isochoric and possibly other factors associated with the crank angle and relative direction of motion between the two pistons.

So, perhaps you could show your actual equation(s), your simply making an assertion is not "proving" anything.

[stephenz]

There is no point trying to drown a fish here.

The compression ratio is a geometric characteristic of any engine, Alpha, Gamma, Beta. "Compression Ratio" is short for "Volumetric Compression Ratio" often detonated as "R" or "Rv". And, as pointed above the ratio of the Min and Max volume. Or its inverse, depending on what book or paper you're looking at.

Don't confuse that ratio with the Pressure Ratio (usually detonated Rp) which is equal to ratio of the Max pressure over the Min pressure.

Rv and Rp are not equal. Among other things Rp takes into account temperature, engine pressurization, when Rv does not take into consideration anything but geometry/dimensions.

My Gamma engine has a Rv of of 1.3, while R is close to 2.0 with an engine pressurization of 90 psi. Only 1.8 at 60 psi. These are actual measurements, not estimations of some sort or values pulled from random internet posts.


Again, an Alpha with a phase angle of 90 degrees, will have typically over 2.0 of compression ratio simply because, there is one specific crank angle at which the engine volume where both pistons are "relatively" close to their TDC, and another specific crank angle at which both pistons are "relatively" close to their respective BDC. The net result of this a relatively small Minimum Volume (compared to a beta or gamma of the same dimensions with 90 degree phase angle) and a relative large Maximum Volume (compared to a beta or gamma of the same dimensions with 90 degree phase angle). Rv = Vmax / Vmin means Rv is naturally greater than that of Gamma or Beta with the same dimensions and 90 degree phase angle (Vmin for alpha is smaller than Vmin for beta/gamma and Vmax for alpha is greater than Vmax for beta/gamma). There is no need to experiment anything, this is geometry - pen and paper is all you'll need. Do it, you got this!!

This will remain true for usable angle (from 60 to roughly 120 degrees).

For completeness in my response you can also look at both extreme phase angles and you'd have:
- at 0 degree phase angle, both pistons have the same TDC and BDC, and since on an Alpha the heads are connected, it means the volume is constant during a full crank rotation. I.e. a compression ratio of 1. i.e. no compression.
- at 180 degree phase angle, both pistons are working against each other and if you assume minimum transfer tube and dead volume, the minimum volume of this configuration would tend to 0, meaning the Ratio Rv gets really, really high.

But then again, neither of these extreme cases will lead to a working engine, so why bother talking about that.


I am only responding here because frankly I am sick and tired of reading non-sense which can't be answered to. And this time, your claim of a Beta having a greater compression ratio than any other configuration is wrong and easily verifiable by basic high school math. Hopefully, you will verify that yourself and admit you were wrong with that specific claim.

[VincentG]

 And this time, your claim of a Beta having a greater compression ratio than any other configuration is wrong and easily verifiable by basic high school math. Hopefully, you will verify that yourself and admit you were wrong with that specific claim.

An Alpha has a geometric compression limit assuming same size cylinders. A Beta does not have this limit, needing only to reduce dead volume and displacer stroke to increase the compression ratio. Especially considering the proposed design where the displacer movement does not lead the power piston.

[Tom Booth]

(...)

Again, an Alpha with a phase angle of 90 degrees, will have typically over 2.0 of compression ratio simply because, there is one specific crank angle at which the engine volume where both pistons are "relatively" close to their TDC,

There is still considerable combined volume in an Alpha with both pistons as near as they can both get, simultaneously to TDC. Rotation from that maximum compression one direction or the other is at constant volume, (one piston going up, the other going down )

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For completeness in my response you can also look at both extreme phase angles and you'd have:
- at 0 degree phase angle, both pistons have the same TDC and BDC, and since on an Alpha the heads are connected, it means the volume is constant during a full crank rotation. I.e. a compression ratio of 1. i.e. no compression.
- at 180 degree phase angle, both pistons are working against each other and if you assume minimum transfer tube and dead volume, the minimum volume of this configuration would tend to 0, meaning the Ratio Rv gets really, really high.

But then again, neither of these extreme cases will lead to a working engine, so why bother talking about that.

There are opposed piston engines where both pistons arrive together at TDC and full compression simultaneously.

I am only responding here because frankly I am sick and tired of reading non-sense which can't be answered to. And this time, your claim of a Beta having a greater compression ratio than any other configuration is wrong and easily verifiable by basic high school math. Hopefully, you will verify that yourself and admit you were wrong with that specific claim.

It should be emphasized, I suppose, that the title of the thread is called Modified "Hot" Beta engine.

Emphasis on POTENTIAL.

At best, even with both pistons all the way at TDC with the crank angle modified an Alpha has the dead volume of the pipe connecting the two cylinders.

Except for the clearance around the sides of the displacer, there is a potential in a (slightly modified) Beta configuration for the volume at TDC to approach zero.

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So there is a real potential there IMO, to have an external combustion engine with a compression ratio comparable with that of a diesel engine or even a fire piston. 20:1 perhaps rather than 2:1

[Tom Booth]

Unfortunately, my efforts at contacting ROCKNTV1 through the comments has had no response, and an email to the address on his webpage came back as undeliverable due to "maintenance".

[stephenz]

 And this time, your claim of a Beta having a greater compression ratio than any other configuration is wrong and easily verifiable by basic high school math. Hopefully, you will verify that yourself and admit you were wrong with that specific claim.

An Alpha has a geometric compression limit assuming same size cylinders. A Beta does not have this limit, needing only to reduce dead volume and displacer stroke to increase the compression ratio. Especially considering the proposed design where the displacer movement does not lead the power piston.

If one is to compare different configurations and their compression ratios, it must be looked at that with some comparable metrics with all pistons/displacers have the same swept volume. And if you do that, Alpha's win in the common usable range.

And I was responding to Tom's general comment that Beta's have the greatest compression ratio of all configurations.

[Tom Booth]

...I was responding to Tom's general comment that Beta's have the greatest compression ratio of all configurations.

First of all, I don't think I ever made any "claim" as you characterize it.

Looking back I see I said:

it just dawned on me a minute ago that a Beta type engine is the most like an IC engine....


...I've avoided the Beta design generally because I don't especially like the idea of having to have a connecting rod pass through the power piston, however, if you want to eliminate the cold side and eliminate dead air space and achieve high compression, I'm not sure there is any better design.

"I'm not sure" doesn't sound like much of a "claim" to me.

All I was saying is that in a fleeting moment of inspiration, I had the idea that out of all the Stirling type engine designs that i know of, the Beta type engine seems most suitable for the kind of modifications I have in mind. Because the piston and displacer move, or could be made to move together, almost as if a single piston, similar to the piston in an internal combustion engine.


So now you want me to admit I was wrong about a supposed "claim" I never made? I could really care less. If you say Alphas have higher compression or whatever, you're entitled to your opinion.

Earlier you wrote:

- at 180 degree phase angle, both pistons are working against each other and if you assume minimum transfer tube and dead volume, the minimum volume of this configuration would tend to 0, meaning the Ratio Rv gets really, really high.

I suppose that could achieve high compression as well. Thanks for pointing that out. Higher than a single cylinder Beta, since there are two pistons. I don't think I'd actually call that a 180° phase angle, seems like 0° since both pistons hit TDC simultaneously, but I guess I know what you mean.


Having two cylinders attached together with no transfer tube hardly seems like an Alpha at that point, but if it makes you happy, I was wrong. I admit it. You were right.

[Tom Booth]

Hey, stephenz.

Since this "alpha" you've invented has the two pistons so close together without a transfer tube, do you think maybe there might be some way to just combine the two pistons in the same cylinder?

Maybe we could have the same compression ratio as two pistons in separate cylinders by just doubling the diameter of the cylinders or something?

I can't really imagine what that might look like though. Probably the pistons would get in each other's way. Never mind. I guess it's impossible.

Wait though, what is we drill a hole in the power piston and put the hot piston's connecting rod right through the cold piston? Nah, that's just crazy, how could that ever work, the connecting rod needs to be able to move from side to side. Besides, then the hot piston would be sealed off from the cold because there wouldn't be any transfer tube.

Never mind.

On the other hand, suppose we left some space or made groves in the side of the hot piston to let the air go through, that could act like a transfer tube couldn't it Stephenz?

But I really just can't figure out all that volume stuff, what is it πRcubed or something? Would you double the size or triple the size of the cylinder?

I'm not really sure what size a standard Alpha cylinder is supposed to be in the first place really, I don't know that much about Alpha Stirlings so I wouldn't know how to increase the diameter when I don't even know what the diameter is to begin with.

Hey Stephenz, what do you think of this idea?

We have this Alpha engine with both pistons in the same cylinder but the hot piston is a little undersize so the air can get around it like a transfer tube and we have the hot piston connecting rod,... Now here is my idea:

Instead of hinging the connecting rod in the center of the hot piston, what if we just have it be straight until it is through the cold piston and then have the joint on the other side of the cold piston?

What do you think?

I don't know if I'm describing this in a way anyone can understand. Hold on, maybe I could make an animation:

output-onlinegiftools.gif (147.16 KiB) Viewed 4394 times

. stephenz's "Alpha" engine

[Fool]

The "first law" thermal efficiency equation is:

Qh=Ql+W

Which I don't have a problem with. It does not imply that work can exceed the heat input, but neither does it suggest that the work output in Joules cannot match the heat input in Joules.

The first law does not forbid the existence of an engine more efficient than the Carnot limit, not at all.

Qh = Qc + W

Or rearranged:

W = Qh - Qc

Second Law:

Efficiency ratio:

n = W/Qh

Or combining first and second

n = (Qh-Qc)/Qh = 1- Qc/Qh

Qh and Qc have a linear relationship to Temperature. Meaning add 100 Joules get 100 K temperature increase. Add 200 Joules get 200 degrees increase.

So they are of the following form:

Qh = Th x Cv + K
Qc = Tc x Cv + K

Y intercept, constant: K = zero because, at absolute zero Kelvin, there will be no heat. Qh and Qc will be zero at zero Kelvin Temperature.

So those two simplify to:

Qh= CvTh
Qc=CvTc

Putting those into the previous equation for n, efficiency:

n = 1 - Qc/Qh

Or

n = 1 - (CvTc)/(CvTh)

The Cv's cancel, becoming one, which leaves:

n = 1- Tc/Th

That is Carnot's Theorem derived from the first and second laws. The first law, conservation of energy, manifests itself into a great many following areas. Maximum efficiency is just one of those.

Here is a more rigorous proof:

Relationship to ideal gas law:

https://en.m.wikipedia.org/wiki/Thermod ... emperature

Scroll down to the appropriate section. It uses a slightly higher level of mathematics.

There are other more complicated proofs should you care for them. It has been proven many different ways.

The Carnot Theorem is just for thermodynamic efficiency. Kinematic efficiency reduces the efficiency even further. And not following the ideal engine cycles, also reduces the efficiency.

Efficiency is a valent goal to pursue, but mostly a waste of effort for a starting concern. Power to weight ratio is a much better pursuit. Think American Drag Racer. 1/4 mile per 12 gallons. 48 gpm. Excellent.