Another Stirling gamma anomaly under the radar

[Tom Booth]

I thought you had it more or less right the first time.

If you have this heat backflow from the sink you guys have been talking about.

I'll have to go back and check, but I thought my correction was right. ...

I confess, I don't really understand your graphs. The hest-in at the sink talk caught my interest though.

Given that expansion cooling leaves the working gas cold at BDC it seems "hysteresis" is unavoidable, but, is it necessarily a bad thing?

Everybody seems to assume "heat rejection" during compression, but how, if the gas is cold after expansion and taking in heat, and a FAST compression is pretty much by definition adiabatic, without heat loss, so, think Fire piston with heat replacement of heat addition/input on the way down.

The heat taken in at/and after BDC is not lost, it is pushed into the hot side for a little extra heat at TDC to power the next expansion.

"Hysteresis" (extra heat) at TDC just gets "recycled".

...an oscillating volume where [heat in=work out during expansion, and work out=heat in during compression]."

But the "work out=heat in from previous "compression".

Say you pull a fire piston out, the gas gets cold and absorbs heat, then drive the piston in. The whole process adds heat for a higher temperature for compression once back at TDC.

[matt brown]

Slightly upthread where I show 'adiabatic' Tdrop for Ian-Hall model, I mention...

Top graphic is a tad misleading, since DP values do NOT coincide PP values (both 'sets' never occur simultaneously) but I'm on track to chasing down work values. In my anomaly thread, I mention that 2 unique temperature volumes have the same heat in and work out during expansion when equal pressure and volume differential (expansion ratio). Therefore, we know that the 300k PP volume/s and 450k DP volume/s will have the same heat in and work out proportional to their volume. So...by frame 3 where DP=600cc and PP=200cc then DP source heat input is 3x PP sink heat input, and by frame 4 where DP=600cc ('unchanged') and PP=400cc then DP source heat input is now only 1.5x PP sink input.

Indeed, ideal mumbo-jumbo, but remember that the 450k DP isothermal source input during expansion does the DP work vs the 450k DP internal energy passes to regen during transfer. We can't simply consider everything as a singular energy where the 450k isothermal input does work then passes thru regen. Nope, the 450k isothermal input disappears as work while the 450k internal energy remains (prior regen).

[matt brown]

I confess, I don't really understand your graphs. The heat-in at the sink talk caught my interest though.

Yes, heat input at sink (ambient backflow) can be far higher than most would imagine. The only really easy gamma calc is compression work since this is a "single" volume (DP and PP) at a single temperature. I'm chasing a way to calc heat in at DP and PP which I'm closing in on (hopefully this week). Meanwhile, I've found...

(1) DP:PP heat input varies by thermal ratio for the same DP:PP ratio (the same physical engine has different gas flow dynamics when the thermal ratio varies, in effect becoming a different engine)

(2) PP must be substantially larger than DP (Vincent's original chase that got me going)

(3) scheme requires regen otherwise DP input will 'short' to PP and nix ambient backflow

(4) all based on ideal distinct events that might be mimed somewhat by unideal events like out-of-phase motion (I'm clueless on that and may never get there)

Given that expansion cooling leaves the working gas cold at BDC it seems "hysteresis" is unavoidable, but, is it necessarily a bad thing?

Likely best considered at the cycle vs process level. My big concern with hysteresis is not temperature, but pressure: (1) as Ericsson and Brayton found out, messing with double-diameter pistons has unique challenges (2) cold gas pools...the gas doesn't jump thru the hoop when we want it to

Everybody seems to assume "heat rejection" during compression, but how, if the gas is cold after expansion and taking in heat, and a FAST compression is pretty much by definition adiabatic, without heat loss, so, think Fire piston with heat replacement of heat addition/input on the way down.

Indeed, both heating and cooling occur at a snail's pace with ECE, but that's part of the challenge. I don't limit my ECE dreams to close cycle 2 chamber valveless designs. Nope, I'm a little more out-of-the-box.

The heat taken in at/and after BDC is not lost, it is pushed into the hot side for a little extra heat at TDC to power the next expansion.

"Hysteresis" (extra heat) at TDC just gets "recycled".

...an oscillating volume where [heat in=work out during expansion, and work out=heat in during compression]."

But the "work out=heat in from previous "compression".

Again, a challenge to figure out what to trade with an eye on practical tradeoffs. Occasionally, a wildcard appears like the gamma which runs off the cold side. This single reality totally changes everything since it nixes any hot engine nonsense.

Say you pull a fire piston out, the gas gets cold and absorbs heat, then drive the piston in. The whole process adds heat for a higher temperature for compression once back at TDC.

The work of pulling the piston out will add some heat during adiabatic expansion whereby more work is now required to adiabatically compress the piston than when first picked up, but the heat vs work energy balance thing remains intact.

[matt brown]

I thought I'd share how I game this mumbo-jumbo...

A 300-450k.png (25.45 KiB) Viewed 2196 times

Here's the original ian-Hall graphic and I'm still trying to figure out heat in vs work out for DP and PP. Knowing that when 2 unique temperature volumes with equal volumes and pressures have the same heat and work values per volume allows total input to be surmised. During this expansion, by frame 4, DPvol=600cc and PPvol=400cc, but thruout this expansion the pressure has remained equal within DP and PP, despite dropping 50%. Once knowing that these heat/work values are equal per volume, we can conclude that by frame 4 the total DP and PP input equals the same input as a 450k isothermal expansion from 600-1200cc. The only difference here is that by frame 4, the 600cc that has left the DP is now only 400cc in PP. This is cool, since I now have a simple way to calc TOTAL input (DP source and PP sink) and only need to figure out how to divide this total (DP vs PP).

Along the way, I also figured out where my "cross-over" point likely lies, simply when PPvol=DDvol...duh.

[matt brown]

Tom - this "cross-over" point is when PP sink input starts exceeding DP source input.

[Tom Booth]

"Say you pull a fire piston out, the gas gets cold and absorbs heat, then drive the piston in. The whole process adds heat for a higher temperature for compression once back at TDC.
__________

"The work of pulling the piston out will add some heat during adiabatic expansion whereby more work is now required to adiabatically compress the piston than when first picked up, but the heat vs work energy balance thing remains intact."

____________



Don't forget that by pulling the plunger, your reducing pressure. So it's basically like stretching a slingshot.

I'm not sure, but I think with a heavy plunger, pulling it out and just letting it go would turn the pressure differential into velocity which then, due to momentum carries the plunger/piston to TDC.

The small amount of heat input at BDC at high RPM doesn't really amount to much, but something. The main point is, heat is not lost during compression.

The "aligning the heat vectors" idea.

Multiple small inputs all converging at TDC.

Think of this guy on a trampoline with six other guys each adding a little extra.

The six helpers hardly do much, just little jumps at precisely the right moment project the guy 40 feet into the air.

The guy is the piston. The trampoline is TDC/main heat input + supplemental inputs at a single point of convergence. "In resonance" driven oscillator.


https://youtu.be/7XgforugkmA



"...an oscillating volume where [heat in=work out during expansion, and work out=heat in during compression]."

But the "work out=heat in from (during) previous "compression"."

[Fool]

If you are accepting the work output from buffer pressure during compression, you must also accept the negative effect of work input from buffer pressure during expansion. Work output during expansion no longer equals heat in during expansion.

P atmosphere fights P gas, by the amount P•∆V atmosphere.

[Fool]

Matt, doubling the ∆V by having a bigger piston just reduces the stroke of the atmosperic PV. Out catches up with in, for no free lunch.

[matt brown]

I think you just caught what I was trying to say, even though I said it poorly. I'll leave you alone. Suffice it to say I meant it a little differently. Sorry.

Fool - thanks for the help, I caught this a few days ago and here's my error...

duplex unbundled.png (7.9 KiB) Viewed 1945 times

I saw a work cheat with ambient buffer, but not in vacuum, so focused on compression half of cycle that I "glossed over" expansion half of cycle. I clearly saw that compression with ambient buffer has less Wneg over lower volume when both volumes are combined, but clearly missed that expansion with ambient buffer has more Wneg under lower volume when both volumes are combined. Yikes, Wpos during expansion over lower volume when separate volumes is gone, whereby the lower volume is no longer the same 'oscillating' volume.

What struck me odd from the start of this duplex distraction is classic 2nd law violation expecting work gain from any single temperature. However, an ideal gamma is nearly a 2nd law violation already ! Oh well, back to the main event...

[matt brown]

Here's a couple graphics that explain my recent equal Q and W per equal V and P, regardless of T...

unequal W.png (14.96 KiB) Viewed 1836 times

Consider above crude Stirling engine cycles where cycle A=300-600k while cycle B=150-300k. The 150k values is merely for convenience and not a cold hole scheme. Note that A and B have equal V and m values, but that Q, W and P values are proportional T.

Now, let's reconsider cycle B where the gas mass m has been doubled: cycle C...

equal W.png (15.23 KiB) Viewed 1836 times

When A and C have equal V with m proportional T, then Q, W and P values are equal. Thus, any 2 equal volumes at the same pressure have equal Q and W values regardless of temperature. This is handy to remember since it will save a lot of time scheming ECE by nixing many schemes early on.

Interestingly, since this is per unit volume (think 100cc) the 2 "equal" volumes can be distinctly different size volumes (I'm avoiding buzz like relative and specific to nix confusion). This is important at a global level since when 2 different temperature masses meet there's little conflict (energy is constant per volume) and any temperature difference merely shifts values around slightly. However, when 2 different pressure masses meet there's some conflict (aka storm) due to different energies per volume. This is why weathermen track pressure, not temperature.

[VincentG]

Lol Matt we all get those blinders sometimes despite our best efforts.

So my question is, as for power output, could ambient back flow into cold piston (with perfect regen) be better than hot connected power piston?

Maybe the high end free piston NASA type engines are taking advantage of the back flow? My initial thought is that their phasing is not ideal enough to make it work.

[matt brown]

Lol Matt we all get those blinders sometimes despite our best efforts.

Yeah, when you're ass deep in alligators, it's hard to remember that the idea was to drain the swamp.

So my question is, as for power output, could ambient back flow into cold piston (with perfect regen) be better than hot connected power piston?

For now, I think so, but this depends upon temperature and volume ratios (thermal cycle and DP/PP vol).

Anyone who's been following this thread should know (by now) that there's no "one size fits all solution". I'm not referring to DIY app, but that PVT values don't "play fair" in a linear fashion. Nope, they move around as if possessed by a strange demon force that defies logic. While chasing those Ian-Hall Q vs W values, I found this comparison which throws another wrench in the crankcase...

Rider-Stirling-Essex.png (14.78 KiB) Viewed 1316 times

This 300-600k cycle is a reality check where I refer to alpha as Rider, cold gamma as Stirling, and hot gamma as Essex. All have the same volume of working gas (again my esoteric 6m) when measured via total volume and charge pressure. Note that Rider 'engine' is 4x either Stirling or Essex, but that expansion stroke is equal for all engines. I drew them all as similar as possible and aligned processes whereby 1-2-3-4 relates to all 3 engines. I'm still studying this, but thought I'd share it, especially since both Stirling and Essex have DP/PP=1 inline Rider hot/cold=1

Note 4 where Stirling 2 bar is lower than Rider and Essex 3 bar. My challenge is to explain this 2 vs 3 bar difference from the same piston geometry. Anyone following this thread should know that by 4 (after expansion) Stirling has source Qin = sink Qin (ambient backflow) when DP=PP while neither Rider nor Essex had any sink Qin.

What I'm finding is that during Stirling (gamma) expansion, working gas transfers to PP via DP expansion then undergoes further PP expansion. The early amount of this total transfer volume has a minor DP expansion and a major PP expansion vs the later has a major DP expansion and a minor PP expansion. Therefore, this total transfer volume is a composite of minor and major expansions within DP vs PP, and summing this is my challenge. Offhand, it might be that both DP and PP expansions explain 2 vs 3 bar after expansion whereby "more work" is achieved than apparent. However, this oddity only occurs when PP vs DP is relatively large.

Once we know that when DP=PP that Source in = Sink in (regardless T values) then we're forced to reconsider traditional 2nd law buzz which nixes Wnet gain when T=constant.

Maybe the high end free piston NASA type engines are taking advantage of the back flow? My initial thought is that their phasing is not ideal enough to make it work.

Poor phasing probably hurts ambient input, but a moot point lacking 'massive' PP vs DP...

[matt brown]

I just found a simple equation to determine the ratio of sink input for any volume and thermal ratio:

(PP/2)/DP+(PP/2)

Thus, for Ian-Hall where DP=600cc and PP=400cc, here's the "worksheet"

(400/2) / 600+ (400/2) = sink ratio
200 / 600 + (200) = sink ratio
200/800 = sink ratio
.25 = sink ratio of total heat input

And when DP=PP then .33 = sink ratio of total heat input, whereby DP source input is (only) 2x PP sink input !!!

There's probably a log function for this that Fool will recognize, but I'm mired in RA and GA.

I'm trying to keep an open mind on this "ambient assist" scheme, but it's getting hard due to classic 2nd law buzz which nixes Wnet when T=constant. IOW using 300k ambient input in PP for Wpos is a free lunch, but this Wpos from ambient input must exceed it's "proportional" Wneg during compression or no free lunch.

[matt brown]

As a longtime alpha guy who came from the steam camp (eons ago), I've always thought the whole gamma-beta thing rather odd with output on the "cold side". At a glance, anyone could say who cares, but some may ask what's happening with regen during expansion. The common conclusion is that this doesn't matter and that any heat of regen is internal energy that will be recycled later in cycle. This sounds plausible and is correct, but there's something else going on during regen that this simple conclusion misses. Let's consider the Ian-Hall model, again...

crude Ian-Hall.png (10.83 KiB) Viewed 1123 times

I'm going to slightly round off some values, but it won't effect the outcome. Starting with compression, the Wneg=30J for 300k 1000cc .6 bar to 300k 600cc 1 bar and this is hard to botch. However, during expansion things are confusing due to 2 volumes with separate temperatures. What I speculate is that the expansion can be considered as a single isothermal expansion from 450k 600cc 1.5 bar to 450k 1200cc .75 bar (despite 1000cc Vmax) which is followed by a partial isobaric compression from 450k 600cc .75 bar to 300k 400cc .75 bar. In this manner, the 'over expanded' transfer volume requires Qin=60J while the partial isobaric compression requires Wneg=15J to 'restore' the 600cc transfer volume (from DP to PP) to 400cc.

Now, everything balances in a crude way except for what drove the isobaric compression ??? Per previous post, I found a simple way to calc ambient vs source heat input and used the Ian-Hall model as an example. This model has .25 ambient input of total which means that 15J comes from PP ambient input while 45J comes from DP source input. Typical Carnot buzz has Carnot=.33 for 300-450k cycle where a 45J expansion input followed by a 30J compression input yields a typical Carnot win. Yet, I'm pitching (so far) that a 60J expansion input (15J free lunch) followed by a 30J compression yields a Carnot loss.

Spoiler alert: this is depressing for any ambient fanboys...

Yes, the 15J ambient input is a free lunch that beats Carnot at first, but this fuzzy 15J isobaric Wneg offsets this free lunch and restores Carnot win just like it 'restores' transferred volume to energy balance. IOW when PP volume increases relative a fixed size DP then the isobaric Wneg during regen also increases. It appears that any cold PP gamma taxes DP output simply due to the isobaric compression during regen. I've always thought that the academic isochoric regen buzz is bogus since the Schmidt analysis always assumes equal pressure thruout engine thus isobaric thru regen (duh).

So, ambient input happens depending upon DP/PP ratio, but doesn't gain anything. However, when lacking regen with a relatively large PP then not only is internal energy lost per cycle, but DP source must make up for 'missing' PP ambient input. I'm only left to ponder isobaric heat out during regen which is 50J in this Ian-Hall example.

[VincentG]

Matt, isn't there another potential ambient input with the constant volume mass transfer going from 4 to 1?