Calculating volume ratios using PV=nRT

[VincentG]

Matt I'm curious as to your take away from that. For me, I see great benefit to having the compression start AFTER peak piston velocity and then decending in velocity towards peak compression.

[matt brown]

This article has a lot of interesting tidbits for 'piston scrapers' (lol). The text next to Fig. 6 is golden. I often use this chart since I often scheme with 4" bore, and 6" stroke is about minimum possible (chart is 4.00 bore with 6.10 stroke, so I love it).

correction...last line should read: I often use this chart since I often scheme with 4" bore, and 6" rod is about minimal (chart is 4.00 bore with 6.10 rod, so I love it).

[matt brown]

Matt I'm curious as to your take away from that. For me, I see great benefit to having the compression start AFTER peak piston velocity and then decending in velocity towards peak compression.

Overall, I agree, but this will likely vary depending upon the particular cycle and mech. My thinking is that, from a mechanical view, the compression should be as short as possible and placed where it does the "least damage". We're all familiar with the typical slider-crank, and many study the sinusoidal effect of rod/stroke ratio on volume, but by adding de saxe "offset" to the mix, everything changes.

[matt brown]

This article has a lot of interesting tidbits for 'piston scrapers' (lol). The text next to Fig. 6 is golden. I often use this chart since I often scheme with 4" bore, and 6" stroke is about minimum possible (chart is 4.00 bore with 6.10 stroke, so I love it).

correction...last line should read: I often use this chart since I often scheme with 4" bore, and 6" rod is about minimal (chart is 4.00 bore with 6.10 rod, so I love it).

2nd correction...last line should read: I often use this chart since I often scheme with 4" stroke, and 6" rod is about minimal (chart is 4.00 stroke with 6.10 rod, so I love it).

[VincentG]

My thinking is that, from a mechanical view, the compression should be as short as possible and placed where it does the "least damage".

This exactly. The compression should hopefully now occur during the last 50 degrees or so of crank angle, but the lower piston velocity gives more time for heat transfer per given RPM. While at the same time the meat of the power is closer to the 90 degree sweet spot of crank angle. Or at least that's my story.

[Tom Booth]

Going with my "paddle ball" analogy, "compression" is "pulling back" on the ball/piston

Overall, I see "expansion" (power stroke) as the "hit" and compression as the "pull back".

I favor a kind of "adiabatic" concept or model where nearly all the energy transfers take place at TDC and BDC.

"Adiabatic" is not really an adequate term.

If I hit a baseball with a baseball bat as it travels over home plate, ALL the energy transfer takes place in an instant so that the force of the swing is instantaneously converted to velocity

Conventional thermodynamic modeling afaik does not delve into VELOCITY as a factor to be considered, but IMO it is the whole goal and purpose of a heat engine, to convert heat into velocity (or in other terms "work" or mechanical motion").

Both the "hit" and the "pull back" take place at the extremes of TDC and BDC. Between those two extremes "work" can be extracted.

Isothermal expansion and compression, on the other hand, is, or would be, more of an incremental push from TDC to BDC and back.

The Carnot cycle is a bit of both.

In either case "compression" starts at BDC when the piston reverses course and the volume decreases.

The question is, how difficult is that compression, and when does it become difficult, or meet resistance and when does that resistance do the least damage or cause the least amount of wasted work.

Using a baseball analogy again, you have the pitch and the swing.

A batter simply tossing a ball in the air and hitting it cannot hit the ball as hard or as far as when it is pitched or thrown at him.

The energy of the pitch and the swing combine at the instant of impact when the bat hits the ball.

So the cooling at BDC is the pitch or "pull back" that sends the ball to home plate and heating at TDC is the hit that sends the ball out of the park for a home run.

So when should the pitch or "pull back", that is 'compression" encounter resistance?

I would say, ideally, not until TDC. The hot, or in other words, never or not at all.

What that would mean is that the cold snap at BDC should be so intense that the pull back, or in actuality, the HIT from atmospheric pressure, the energy of the pitch, will ALL be converted to VELOCITY which will ALL be converted to combined VELOCITY at TDC.

In other words, the "hit" or heating at TDC should be delayed as long as possible and be as focused and concentrated AT TDC as possible.

In practice, due to various constraints, this would probably need to be fudged somewhat to get the maximum "alignment of heat vectors" at TDC but...

Isothermal expansion and contraction, in its "ideal" forms is "quasistatic". Zero velocity.

[VincentG]

The question is, how difficult is that compression, and when does it become difficult, or meet resistance and when does that resistance do the least damage or cause the least amount of wasted work.

This is the key takeaway. If compression resistance is delayed as late as possible BTDC, the "spring effect" is nearly returned after TDC. So if the cold return stroke can supply the energy needed to pass through compression, then the effective cylinder pressure contributing to piston velocity after TDC is actually the measured in cylinder pressure minus 1 atm.

Internal pressure TDC @300k= 29psiThis pressure represents a 2 to 1 compression ratio
Internal pressure TDC @600k= 58psiThis pressure represents 2 to 1 compression plus a 1 to 2 temperature ratio gain
Net hot stroke pressure= 29psi!!

So here the "net" hot stroke pressure would actually be 29+29-1atm=43psi instead of only 29.

Consider that with this 4 to 1 engine model, in cylinder pressure is below atm at 55 degrees before BDC, even at 600k. So when the hot plate is obscured by the displacer, there should be a significant expansive cooling effect. Separate from any cooling from work output after TDC, which I intend to combat with constant application of heat until some(unknown as of now) degree before BDC.

Tom's thoughts about aligning heat vector's is significant here and will surely take some trial and error to get right.

I think there will be even further temperature gain(and loss) from the period of near constant volume heat addition(and removal) at TDC(and BDC). This perhaps is based on my misinterpretation of this excerpt from the Stirling Engine Design Manual by William R. Martini

As the gas is transferred at zero total volume change from the cold
space to the hot space the pressure rises. This pressure rise results in a
temperature increase in the gas due to adiabatic compression.
Therefore, at the end of the transfer process the mixed mean gas temperature
in the hot space will be higher than 900 K. Point 3 is calculated for all the
gas to be exactly 900 K. Adiabatic expansion then takes place. Then by the
same process as just described, the transfer of the expanded gas back into the
cold space results in a lower gas temperature than 300 K at the end of this
stroke. The computational process must be carried through for a few cycles
until this process repeats accurately enough. This effect will be discussed
further in Section 5.1.6.

[matt brown]

What Martini is referring to is often called regen 'flutter' and here's the basic issue...consider an ideal Stirling cycle and alpha engine with theoretically prefect constant volume transfer between cold and hot cylinders. With this imaginary alpha, each piston has a linear motion where each volume APPEARS ideal, however, as the cold volume transfers into the regen and starts heating up, this temp increase 'retards' the cold gas flow thru regen into hot cylinder. Now, if we continue to assume prefect constant volume relationships, the gas density in cold and hot cylinders will be proportional to absolute temp in each cylinder, whereby the hot gas is compressing the cold gas during regen (aka cold gas 'pools'). This is most noticeable with high thermal ratios (note Martini's 3:1 ex) but also an issue with high volume (compression) ratios.

I'm very familiar with this issue, and curious what Stephenz would discover with his computer sims.

[matt brown]

Now here's where it gets really amusing...this flutter can be considered an example where the temp differential drives a density differential which alters pressure vs simple theory, but this also allows the pressure in both cylinders to remain equal (Schmidt assumptions). So, take this as temp effecting pressure, but Tom hit on another obscure issue awhile back where the volume between the hot and cold spaces can effect the temp, whereby the hot gas passing to cold space increases temp vs theory, and the cold gas passing to hot space decreases temp vs theory. This doesn't always happen (depends upon combined PVT values) but very astute that Tome caught this.

[VincentG]

Still, how does that explain the increase over the 900k heater temp? Maybe I should go back and see if I missed something in the paper.

[matt brown]

The question is, how difficult is that compression, and when does it become difficult, or meet resistance and when does that resistance do the least damage or cause the least amount of wasted work.

This is the key takeaway. If compression resistance is delayed as late as possible BTDC, the "spring effect" is nearly returned after TDC. So if the cold return stroke can supply the energy needed to pass through compression, then the effective cylinder pressure contributing to piston velocity after TDC is actually the measured in cylinder pressure minus 1 atm.

I need to read a few threads a few more times, but offhand, here's how I see this...

Consider a single cylinder engine with single-acting piston and slider-crank, but allow everything else to be imaginary. if you can delay compression AND expansion as long as possible, then MEP on upstroke decreases and MEP on downstroke increases.

Did you ever see the double-acting stepped piston "Loud Mouth" engine in Popular Mechanics many decades ago ??? It was the cover story in late 1950s as I recall (I have a copy somewhere) but basic scheme actually dates to the early 1900s.

[matt brown]

Still, how does that explain the increase over the 900k heater temp? Maybe I should go back and see if I missed something in the paper.

I never read anything by Martini, but I'm guessing he's merely pointing out that any 'redistribution' of gas must be adiabatic when constant volume, and a workless expansion that taxes efficiency.

[VincentG]

Consider a single cylinder engine with single-acting piston and slider-crank, but allow everything else to be imaginary. if you can delay compression AND expansion as long as possible, then MEP on upstroke decreases and MEP on downstroke increases.

Thats a good way to put it. It's like the spring motor video posted back on page 2, but with an extra kick after TDC.

Did you ever see the double-acting stepped piston "Loud Mouth" engine in Popular Mechanics many decades ago ??? It was the cover story in late 1950s as I recall (I have a copy somewhere) but basic scheme actually dates to the early 1900s.

Nope but I found the digital archives online so I'll try to find it.

The Martini thing, to me, seems to be suggesting a possible increase in efficiency that was actually discounted in the analysis. In my eyes, the gas when heated at constant volume, tries to occupy more space but can't so pressure increases. The pressure increase from the fixed walls squeeze back on the gas causing a further increase in temperature. Similarly but conversely, when an air compressor piston compresses air, the gas wants to occupy the same space, but can't, so the pressure rises. The rise in pressure causes an increase in gas temperature. The gas molecules don't know whether a piston is reducing volume, or a fixed wall is not allowing a volume increase, IMO.

On the cold side of things, I think the effect could be even more significant. When cooled at constant volume, the gas tends to contract and take up less volume, but is simultaneously allowed to expand into the same original volume. This contracting, while being allowed to expand, could cause the temperature to go below the cold sink value as Martini suggested.

[matt brown]

Now here's where it gets really amusing...this flutter can be considered an example where the temp differential drives a density differential which alters pressure vs simple theory, but this also allows the pressure in both cylinders to remain equal (Schmidt assumptions). So, take this as temp effecting pressure, but Tom hit on another obscure issue awhile back where the volume between the hot and cold spaces can effect the temp, whereby the hot gas passing to cold space increases temp vs theory, and the cold gas passing to hot space decreases temp vs theory. This doesn't always happen (depends upon combined PVT values) but very astute that Tome caught this.

Yikes, I got that wrong...as I now recall, Tom suggested that the gas passing from hot space to cold space could become cooler than cold space whereupon cool space 'heats' it somewhat, and vice versa. Tom, let me know if I got that right...

[Tom Booth]

Now here's where it gets really amusing...this flutter can be considered an example where the temp differential drives a density differential which alters pressure vs simple theory, but this also allows the pressure in both cylinders to remain equal (Schmidt assumptions). So, take this as temp effecting pressure, but Tom hit on another obscure issue awhile back where the volume between the hot and cold spaces can effect the temp, whereby the hot gas passing to cold space increases temp vs theory, and the cold gas passing to hot space decreases temp vs theory. This doesn't always happen (depends upon combined PVT values) but very astute that Tome caught this.

Yikes, I got that wrong...as I now recall, Tom suggested that the gas passing from hot space to cold space could become cooler than cold space whereupon cool space 'heats' it somewhat, and vice versa. Tom, let me know if I got that right...

Well, I was just about to post a response to your attributing that to something I had said somewhere. What? Where did I ever say that?

But thinking on it again now,...

You have compression between BDC and TDC but 90° before TDC the displacer moves which way?

You had me confused there for a moment. If the displacer moves from the hot side to the cold side then do you have cooling taking place before full compression? I had myself wondering if I had said or implied any such thing.

But no, if the displacer moves TO the cold side it exposes the hot side and so heat is added, so no, cooling does not happen at TDC, but then...

Yes, I did say that since heat is added and heat of compression combined with that, the combined heat could drive the working fluid to a temperature above the hot side heat source temperature and that this could cause a "heat pump" effect where heat could transfer from the working fluid back into the heat source.

What you wrote though:

, but Tom hit on another obscure issue awhile back where the volume between the hot and cold spaces can effect the temp, whereby the hot gas passing to cold space increases temp vs theory, and the cold gas passing to hot space decreases temp vs theory.

Is worded in a way that doesn't really make sense to me nohow.

But then, yes, with expansion/cooling 90° Before BDC the DISPLACER moves to the hot side, (which exposes the cold side) so you have a compounding of the cooling so the working fluid could become colder than the "sink" so as to draw heat out from the cold side, which for an instant, causing the engine to function as a heat pump.

So.... "the hot gas passing to cold space increases temp" is kind of accurate but leaves out some details that makes it misleading.

The hot gas while being expanded and also moving to the cold space simultaneously (and also outputting "work") results in such extreme cooling that heat can be taken in from the cold sink, which actually, at that point "increases temp"?

Well,...

The temperature of the working fluid DECREASES so that it can take heat away from the sink.

So, if the working fluid is absorbing heat, taking heat away from the sink, is the temperature of the working fluid then INCREASING?????

Well, the working fluid in a refrigerator is expanded in the evaporator becoming so cold it absorbs heat from the ice box. So, in getting so cold as to absorb heat does it then increase in temperature????

I would tend to imagine that the working fluid cools and continues cooling due to the expansion and work output, though at BDC may absorb some heat AS IT CONTINUES TO COOL, or maybe the cooling levels off, or at some point, does the temperature actually increase as a result of absorbing heat from the cold "sink"?

Also with compression in a refrigerator the working fluid gets hot so it can release heat to the warm surroundings. So in getting hot under compression does it then cool??? Or cool as it gets hotter???

Well,... Sort of, maybe. But I think this is a case where absorbing and releasing heat does not necessarily equate with heating up and cooling down.

During compression the gas gets hotter. Then relative to the engines heat source it could lose some heat to the heat source very briefly but it is likely still getting hotter due to continued compression, at least until after TDC.

Or perhaps at exactly TDC compression stops and the working fluid is still hotter than the engines heat source so at that instant there could be cooling of the working fluid if you "freeze frame" the action at that exact moment in time.

So, your initial characterization of what I said has some truth to it, I think.

It is an interesting conundrum anyway.

Does the gas cool as it heats up? Then, by getting cold, does it warm as it takes in heat due to being so cold?