Alpha stirling engine working principle

[jpigg55]

Forgive me if this is a repeat. I used the "Search" function, but always got the same "too common term" results.
I worked for 36 years in the nuclear energy field with 6 years in the US Navy and 30 years in commercial nuclear power plants as a mechanic and operator, thus I have a very good understanding of thermodynamics and mechanical operating principles.
This made it fairly easy to understand how Beta, & Gamma Stirling engines work, but struggled somewhat on the Alpha engine.
While the Alpha is a differential heat engine working, at least partly, on the expansion and contraction of the working gas, I had trouble getting past the concept that the force acting on the pistons was equal due to the equivalent surface area.
After much thought, the conclusion I came to was there was something else at play. I concluded the was (what I term as) a "differential leverage" working principle derived from the 90 degree offset of the connecting rods wherein the force acting on the crank from the pistons differed during rotation.
Can anyone point me to threads here or links elsewhere that can put new light to my understanding ?

[Bumpkin]

I've never seen it explained well, and this probably won't help; but I'll take a stab at it:
Visualize a single-crank-pin 90 degree V twin Alpha. Minimum volume is the crank centered at 45 degrees between the cylinders and maximum is 180 degrees further along, similar to tdc to bdc of a Gamma power piston. Then consider the placement of the air between the hot and cold ends of an Alpha as similar to the air in a Gamma displacer chamber. At first glance, it looks like the Alpha placement change is only leading the volume change by 45 degrees, but I think you can add to that the 45 degree average of the two pistons working for and against each other; as you said, differential leverage (and differential volumes.) Clear as mud, right?

Bumpkin

[matt brown]

While the Alpha is a differential heat engine working, at least partly, on the expansion and contraction of the working gas, I had trouble getting past the concept that the force acting on the pistons was equal due to the equivalent surface area.

Xlnt observation which many miss or discount due to other issues. Even with the common assumption (Schmidt analysis) that the pressure is equal thruout engine at any given time, the force on identical alpha pistons is not due to crankpin location (bellcrank effect).

After much thought, the conclusion I came to was there was something else at play. I concluded that was (what I term as) a "differential leverage" working principle derived from the 90 degree offset of the connecting rods wherein the force acting on the crank from the pistons differed during rotation.

Most SE guys are in the gamma/beta camp, but I'm an alpha fanboy for various reasons. SE mindset is loaded with various falsehoods that allow guys to carry the torch, but get nowhere. Your 'differential leverage' is a perfect example where the common assumption is that Wpos vs Wneg per piston can be simply summed per cycle (rpm) whereby these force issues cross-cancel during rotation. This isn't true with ICE, so why would anyone assume this is true for SE ?

One reason I favor the alpha is simply for your callout where an ideal alpha with pistons/slider-crank/90deg phasing has expansion start at 90 deg near torque max vs similar ideal gamma where expansion starts with PP at TDC. If new to SE, these mechanical issues are dwarfed by numerous thermo issues. Another reason I favor alpha is that each cycle (rpm) ideally uses entire gas mass for output vs gamma/beta rarely exceed 2/3 before regen and commonly around 1/2. So, gamma/beta require far more regen per gas mass than alpha which is no problem when regen=1.0 except for relatively larger regen. However, as regen efficiency declines from 1.0 this thermo "differential" will dwarf most mechanical issues due to regen "load"...the ratio of ideal heat of regen divided by ideal heat source input (where regen>source).

Can anyone point me to threads here or links elsewhere that can put new light to my understanding ?

I've seen studies in past, but can't recall any, offhand.

[Tom Booth]

Can anyone tell me where or when Alpha type "Stirling" engines originated?

They don't appear, afaik, to have originated with the Stirling brothers.

Also, I don't think I've ever seen an actual "pure" V type Alpha that actually works, without modifying the original(?) concept and making one of the pistons basically function as a displacer.

[matt brown]

AFAIK the first alpha is credited to Alexander Rider in 1875, but often referred to now as the original Rider to distinguish it from a later Rider engine. The original version had two distinct cylinders vs later version had a single cylinder and effectively a beta. Adding to confusion is Rider-Ericsson company name which is a small history in itself. Here's the original Rider which forum member "spinnmagnets" posted recently

Rider.png (277.83 KiB) Viewed 8043 times

The is my favorite hot air engine of past.

[matt brown]

Here's a screenshot of some alpha links, note one on right and bottom where heater and cooler are between regen and cylinders...

alpha links.png (267.07 KiB) Viewed 8040 times

[matt brown]

While the Alpha is a differential heat engine working, at least partly, on the expansion and contraction of the working gas, I had trouble getting past the concept that the force acting on the pistons was equal due to the equivalent surface area.

Xlnt observation which many miss or discount due to other issues. Even with the common assumption (Schmidt analysis) that the pressure is equal thruout engine at any given time, the force on identical alpha pistons is not due to crankpin location (bellcrank effect).

edit: my last sentence should end...the force on identical alpha pistons is not [equal] due to crankpin location...

[jpigg55]

edit: my last sentence should end...the force on identical alpha pistons is not [equal] due to crankpin location...

The combination of factors, to me, is where it gets tough to wrap ones head around. Each component is fairly easy, but the combination starts to muddy things up.
From just the piston perspective, both pistons are of equal diameter, and thus surface area, in an Alpha SE. The "Ideal Gas Law" tells us that pressure=force/area or, put another way, force=pressure x area. Since the pressure acting on the pistons is equal, the downward force on each piston is equal.
From the perspective of the crank, this is where "Torque" comes into play. The effective "lever" length gets longer as rotation moves from 0 (TDC) to 90 degrees with max torque at 90 degrees rotation.
Now we get to the "Work" & "Acceleration" parts of the equation. Work=Force over some distance and Acceleration being the rate of change of the change in distance. This depends on the type of connection between the piston and crank that also doubles as the means of conversion between linear motion and rotational motion. The 2 types I'm aware of are the Connecting Rod and the Scotch Yoke.
Here again, we run into a perspective issue. Like an ICE, the piston moves a greater distance in the first 90 degrees of rotation than in the second with a crank pin connection for a given crank shaft RPM. This is what defines the acceleration of the piston in that the piston spends more time/travel distance in acceleration than it does in deceleration. Conversely, the acceleration/deceleration travel distances of the piston are equal with a Scotch Yoke connection configuration.
Now we add in the second piston with the 90 degree connection offset. This is where things get muddy for me. Trying to envision where in the rotation angle that equates to max and min volume, torque, and work of the system exists.

[Fool]

The way I think of the Alpha engine is that the two pistons work in concert to increase volume and decrease volume.

If most of the heat is applied during most of the expansion, it will speed up the engine.

As the opening post said, "lever action", from the difference in crank positions makes a preferred direction. Yes. The pressure in both cylinders is approximately the same for the same force on both pistons.

If most of the cooling happens during the compression stroke, less energy is wasted during the return compression stroke.

[spinningmagnets]

Part of the 90-degree separation between the pistons is the lag-time for the gasses to absorb and shed heat. You "could" separate the pistons by 180-degrees, so all of the gasses are in the hot side or cold side, but then you'd need a third piston to use the gas temp change to spin the thing.

xxxxxxxxxxxxxxxxxxxxxxxxxxxx

I've come to appreciate recently that the Rider derived significant benefit from orienting the engine to have two parallel vertical cylinders, and it uses heavy pistons "on purpose". I don't recall the reference, but after manufacture, the engine could be fired up by the customer and they could slowly add weight to the inside of the pistons (molten lead?), until a they find a point where the engine runs more smoothly.

As we have seen on the internet, Alpha-Stirlings can be built with horizontal cylinders, and they can also have the cylinders in a 90-degree V-configuration. However, the vertical cylinders with the crank located on the top mean that the heated internal gas lifts both the pistons (again, 90-degrees apart) but them they are falling when the gas is cooled. This means that the design uses the weight of the pistons falling to apply two power pulses.

If this is correct, then the Rider applies four evenly-spaced power pulses to the crank per rotation, rather than the obvious two that come from heat expansion.

[Tom Booth]

Only observing animations your "differential leverage" observation makes sense in that after the hot piston moves back exposing the hot sides of the hot cylinder, (assuming there is actually a heated hot cylinder as in most animations, Matt has said this is not usually the case, but it's how these engines are frequently depicted)... The hot piston had reached the end of its cylinder so can go no further. As the working fluid is still fully exposed to heat input, the only thing that can move any further is the other cold piston.

Conversely, during the cold phase when most of the working fluid is in the cold cylinder, the hot piston is not able to move as it is in line with the crankshaft and so cannot move up or down the cylinder in this position, so as the gas "contracts" again, only the cold cylinder is able to respond to the pressure differential having more freedom of motion at that instant.

In other words the hot piston functions much like a displacer, exposing the working fluid to heat, but once it does so fully becomes "locked in position". Likewise after the working fluid is pushed to the cold side the hot piston is again at the end of its travel in that direction and can move no further, but the cold piston is again free to move in the opposite direction.

The cold piston acting almost like a kind of double acting power piston.

The hot piston really does little more than brace itself giving all the mechanical advantage to the cold "power piston".

[matt brown]

I'm a longtime alpha fanboy who favors basic Rider with upgrades. The main issue with the Rider is the entire notion of heating the working cylinder which is why I find gammas interesting. Here's my spin on alpha advantages:

(1) with ideal phasing (whatever that entails) a typical 2:1 compression slider-crank/piston configuration will have expansion start near max torque of crank (bellcrank effect)

(2) with 2:1 volume ratio and typical DIY 300-600k cycle, regen 'load' is only 1.0 input vs typical gamma is usually 1.5/+ for low end designs and 3/+ for high end designs. Every 1% loss in regen will be multiplied thru this regen load factor. So with good regen=.95 that meager .05 loss can easily knock .15 off ideal output, but this .15 loss taxes a high eff engine more (absolute) than a low eff engine. You can reduce this 'load' loss by simply switching from diatomic air to monatomic helium (as if by magic) but this brings in only issues.

(3) within DIY 'market' alphas have the best potential to repurpose mechanical parts (ICE, compressors, etc)

Alphas might be the easiest to design and build, but they remain the hardest to get running. Even after many years studying these buggers, I'm unsure why, but my best guess is lame phasing which leaves the engine (think pistons) fighting itself.

Good catch Tom on the animation where most of the ideal constant volume transfers are lost amidst real out-of-phase pistons.

[Tom Booth]

....
Good catch Tom on the animation where most of the ideal constant volume transfers are lost amidst real out-of-phase pistons.

I'm not sure what I caught that is described by what you just said.

"Ideal constant volume transfers"? "Lost"?

I can't say I caught that, really, as I don't know what your talking about. I don't know much about Alphas, just observing the animation and noticing how they APPEAR to work. When the piston, connecting rod and crank are all in line, it is impossible for the piston to move up or down the cylinder.

The other piston can, though, so not constant volume.

I have an aversion to most anything "ideal" supposedly related to how an engine operates. It all seems like unrealistic pie in the sky nonsense dreamt up by academics who have no real clue about actual mechanics.

[VincentG]

In a good running Alpha, the hot piston is the prime mover. The cold piston being pressured back towards BDC is just a flaw in phasing(as often pointed out by Matt) and is hopefully avoided.

[Tom Booth]

In a good running Alpha, the hot piston is the prime mover. The cold piston being pressured back towards BDC is just a flaw in phasing(as often pointed out by Matt) and is hopefully avoided.

I've come to take just about anything Matt says as intentional sabotage or a red herring.

If you want a Stirling engine that works and get advice from Matt, do the opposite.