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Whoa Vincent, good catch !!! Yeah, assuming ideal 600cc regen from 450-300k then P drop in PP from .75 to .6 would suck in more ambient heat. Jeez, them blinders again - LOL

My main focus has been in chasing down the big things knowing that there's still lots of small things. Look back upthread at that Rider-Stirling-Essex graphic and compare Stirling 4 to Essex 1. I'm now wondering what's going on during Essex compression vs Stirling expansion...is there some isobaric mumbo-jumbo going on with Essex compression also ???

The other thing I'm wrestling with is how to reconcile my Stirling isobaric regen theory with other regen schemes. IOW is isothermal expansion DURING regen the culprit vs 'simple' Rider regen ? My isobaric regen loss theory is similar this...


The "stair stepping" here is to explain integrals, but I'll borrow the graphic. However, for my isobaric regen loss theory, I use a horizontal zig-zag between 2 curves in this stair stepping region that represent the isobaric backwork via tiny zig-zag near apex that horizontally expands towards the bottom (1) upper curve from apex representing the total isothermal work 600-1200cc (Ian-Hall model) and (2) lower curve from apex representing progressive isobaric backwork during this expansion. The first curve ends at 1200cc, the second curve ends at 1000cc, and the area within should be my isobaric work loss (this really needs a white board video). I found the ambient input from simple geometry using equal input per cc and triangulation (linear isothermal progression cross-cancels those sexy integrals).

Matt, I’ll review and comment later, but for now that graphic and this discussion is exactly what I was thinking about in the thermodynamic work v. real work thread.

The area under the curve is misleading as it represents a changing buffer pressure, and that’s just for starters.

Another graphic that will clarify several issues...


Note sign convention where - is work-in or heat-in while + is work-out or heat-out (joules). This is the same graphic as recent Rider-Stirling-Essex except I nixed Rider and added 'space' to each volume since 300cc is more convenient.

The question arose recently about gamma expansion vs Essex compression where both appear voodoo vs simple Rider. The Essex compression process is akin the 300cc PP volume being compressed to 150cc isobarically, then this 150cc PP volume AND the 300cc DP volume being further isothermally compressed. When comparing the W and Q values for this compression, notice that the work of BOTH these compressions is close to half the work of expansion and clearly inline Carnot=.50 for an "isothermal" 300-600k cycle. Unbundled this way there's no mystery to Essex/values.

Moving to the gamma expansion, my isobaric regen theory has this process similar 300cc DP volume being expanded to 900cc isothermally akin 300cc in DP and virtual 600cc in PP, then this virtual 600cc volume being isobarically compressed to actual 300cc PP volume. However, both these processes occur together (on the fly) vs distinct events. In this manner, the total DP volume that transfers to PP has 2 expansions, one in DP prior transfer and one in PP after transfer. My work values show +198 isothermal expansion with -60 isobaric compression whereby Wnet for this expansion = 138 and very similar Carnot=.50 for an "isothermal" 300-600k cycle. I previously claimed ambient input=.33 when DP=PP which would be ~65 for this expansion. I'm clueless why these values aren't closer, but let's just go with these, so this wouldbe ~65 ambient input "equals" the isobaric work loss, otherwise this simple gamma would be Super-Carnot.

Hmmm, the isobaric Essex compression is driven by a piston/flywheel and straight forward once explained, however the isobaric gamma compression is driven by the isothermal DP expansion. Both of these isobaric compressions will require work in (no free lunch here) and will generate massive Qout vs 'similar' isothermal compression simply due that isobaric processes involve a change in internal energy. However, looking at those massive Qout values for both of these isobaric processes, don't worry that this Qout is lost to sink, since most will be sucked up during regen.

My current isobaric regen theory is that the internal energy equivalent passes to regen while the work equivalent passes thru regen (overloads regen, heads to sink, whatever you prefer) and ends up in PP prior anywhere else. And guess what is waiting there during this crazy process??? Yep, an expanding Tlow gas looking for input !!! I have a creepy feelin' that the work of this isobaric gamma compression equals the heat deficit from this isobaric compression and ambient input never occurs (when ideal). However, if you nix regen, then any gamma is a waste of time.

This anomaly thread would have been short and coherent if I had waited until now, but I didn't know how far I could get, so I thought I'd throw it up as a work in progress and share my wild ride. Previous post is getting close to issue, but calc method still needs work. Anyways, the bottom line is amusing...

Fool wrote: ↑Fri Aug 23, 2024 7:04 am Your processes show how expansion has three competing events. In the hot zone expansion is at Th constant temperature. In the cold zone expansion is at Tc constant temperature. In the regenerator expansion is 'between' with heat loss and expansion happening simultaneously, (as Happy Quinn says.) 'not good'. The complexity of these engines always seems to amaze me.

Everything correct except that...in the regenerator ISOBARIC COMPRESSION is between with heat loss and expansion happening simultaneously, 'not good'.

Early in this thread, I posted this graphic


The anomaly is 'clearly' shown here, but I glossed over it as a mere coincidence since PVT values between hot vs cold PP gamma appear chaotic when thermal and DP/PP ratios change. I had data overload and couldn't reduce anything to valid conclusions. So, I got creative and tried using distinct transfer volumes (interesting) before I got crazy and tried using 'isolated' volumes (amusing, but lame).

This thread started 1-1/2 weeks ago, but 6 months ago, I pitched the same thing in a short thread entitled "Why Stirling engines have low power and efficiency" where this graphic had the same conclusion. Unfortunately, this graphic compared Essex to Stirling where Essex DP=PP, Stirling DP=Essex DP, and Essex PP>Stirling PP (in this 300-600k ex, Essex PP was 2x Stirling PP). If only I had made Essex PP=Stirling PP and Stirling DP>Essex DP.

http://www.stirlingengineforum.com/view ... 554#p21554

Here's a current graphic that shows this "anomaly" clearly...


Comparing Stirling A with Essex, we can only guess what's up with lame Stirling A 2 bar in frame 4. Now, compare Essex vs Stirling B where P values Essex 1-2-3-4 equal Stirling B 1-2-3-4 then compare V and m values of Essex 3-4 vs Stirling B 3-4. It should be obvious that for this 300-600k thermal cycle that Stirling B uses 2x Essex input FOR THE SAME OUTPUT and this is what I've been chasing !!! I'm convinced that (1) Stirling regen involves isobaric compression between isothermal DP expansion and isothermal PP expansion where 'most' of the isothermal DP Wpos is lost to isobaric regen Wneg (2) during this isobaric regen, 'some' of the heat of compression becomes isothermal PP Wpos (3) no ambient sink input (backflow).

Therefore, the Stirling cold gamma PP is total BS (this Essex has 2x the efficiency of Stirling B). The few hot gamma studies I've read are missing this, and must consider all Stirling regen isochoric. I can only wonder whether any of these guys ever built a model, tested it, then wondered where all the anticipated output went.

So, Vincent is right, the Essex kicks ass over Stirling...

If your point is that all the expansion needs to be in the hot zone, and all the compression needs to be in the cold zone, and the regenerator volume needs to open for heat transfer, and close for volume change. I get your point.
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Therefore, the Stirling cold gamma PP is total BS (this Essex has 2x the efficiency of Stirling B). The few hot gamma studies I've read are missing this, and must consider all Stirling regen isochoric. I can only wonder whether any of these guys ever built a model, tested it, then wondered where all the anticipated output went.

If your point is that all the expansion needs to be in the hot zone, and all the compression needs to be in the cold zone, and the regenerator volume needs to open for heat transfer, and close for volume change. I get your point.

Matt, I appreciate all the time and effort you have put into this, especially if it was in part due to my sometimes nonsensical rambling. I wonder a lot if I'm wasting my time on these things, but it seems you have found something worth finding with your studies. Rereading this, it deserves to be condensed into a dedicated research paper and I hope you may find the time to do that.

So what's next?

Vincent - thanks for the nod and back at you. Had it not been for your fresh set of eyes exploring conventional issues, I never would have started my gamma deep dive. Then your Essex illuminated some unconventional issues that were under the radar. My approach was via ideal gas law, but this becomes clumsy beyond narrow comps. Nevertheless, this method worked, but I now think that there's a simple "academic" proof against cold gamma PP. Hopefully, I can refine all this into a short read with major 'accessibility' despite that my last graphic should suffice to convince most DIY Stirling fanboys...

VincentG wrote: ↑Fri Sep 13, 2024 10:57 am
So what's next?

Over recent decades, Stirling buzz has become a catchall for any hot air engine. Granted, hot 'air' engine is a poor term as is external 'combustion' engine, but if we restrict "Stirling" engine to a mandatory cold PP distinction then everything makes more sense. In this manner, the Rider is no longer a "Stirling alpha" and the Essex is no longer a "hot gamma".

I'm not down on ECE, just 'Stirling' and suggest no one waste anymore effort chasing cold PP pipe dreams. In retrospect, we should have known that any scheme which defies a simple PV is sketchy and probably best avoided. I think this whole Stirling chase was fed by treehuggers and grantmeisters, each with their own agenda. This nonsense has been going on for 50 yrs, but begs the question whether anyone really knew that the Stirling cycle was this lame. I'll try to reach Senft for his take on this and let you guys know if I get any reply. It's quite possible that this "anomaly" was missed since most Stirlings have DPvol far greater than PPvol and this may have blinded numerous researchers. Even with the best intent and fancy computer sims, garbage in=garbage out, so it's quite possible that this regen Wneg slid past 'under the radar' and masqueraded as regen inefficiency. However, any half-ass sim should have raised red flags when run 1.0 Cv regen. As for actual tests, any research model with real input and output values might simply blame poor regen for poor results which has been a recurring theme for decades.

So, where do we go from here ??? Simple, forget any cold PP scheme and focus on hot PP schemes only. I've been a hot PP fanboy for decades and my favorite legacy hot air engine is the Rider. I used to wonder how Stirlings made power on the "cold side" vs the "hot side", but never explored this mystery until recently. Hmmm, mystery no more, just voodoo...

If Fool is still following this thread, I expect he's waaaay ahead of me and running calcs on this 'anomaly' as nothing more than a change in enthalpy (rare buzz for single phase gas).

I may have spoken too fast regarding nixing cold PP chase despite inherent isobaric regen Wneg. Consider the following 2 recent graphics which contrast the same Stirling vs Essex output per graphic, but from different thermal cycles.

In the 1st graphic, Stirling B and Essex have equal expansion Wout from equal PPvol, but Stirling B requires 2x Qin vs Essex. Note several things here (1) this thermal cycle is 300-600k aka thermal ratio=2 whereby (2) Stirling B requires DPvol/PPvol=2 vs Essex gets by with DPvol/PPvol=1 thereby (3) Stirling B has 2x m (gas mass) in 2x DPvol vs Essex.

Meanwhile, in the 2nd graphic, the Ian-Hall Stirling and Essex also have equal expansion Wout from equal PPvol, but Ian-Hall Stirling now only requires 1.5x Qin vs Essex. Hmmm, note several things here (1) this thermal cycle is 300-450k aka thermal ratio=1.5 whereby (2) Ian-Hall Stirling requires DPvol/PPvol=1.5 vs Essex thereby (3) Ian-Hall Stirling has 1.5x m (gas mass) in 1.5x DPvol vs Essex.

Thus, when Essex and Stirling have equal PPvol (and dP is equal) then expansion Wout is equal. However, the Stirling will require DPvol/PPvol=thermal ratio AND Stirling Qin/Essex Qin will equal the thermal ratio. But let's consider this another way. Assuming a 300-600k cycle with ideal Carnot=.50 then Stirling shrinks by 1/2 to eff=.25 simply due to 2x real Qin vs ideal Qin. Yeah, a nasty tax, but a 300-450k cycle with ideal Carnot=.33 has Stirling shrink by only 1/3 to eff=.22 due to 1.5x real Qin vs ideal Qin.

IOW if 300-600k Essex has eff=.50 then Stirling has eff=.25 (Essex has 2x Wpos from same Qin)
but when 300-450k Essex has eff=.33 then Stirling has eff=.22 (Essex has 1.5x Wpos from same Qin)
Yikes, in this manner, the Stirling increases real eff by merely lowering it's thermal ratio !!!

Stirlings definitely favor low thermal ratios since this reduces the isobaric compression Wneg in regen during isothermal expansion Wpos (DP and PP).

Vincent will probably catch that the Stirling DP/PP ratio is converging with the thermal ratio and that DP/PP=1 equates with 300-300k thermal cycle, but that this appears to be a thing apart from any actual compression ratio.

I'm pretty sold on hot PP Matt. Though nothing I'm working on is true hot PP like the Essex, more like medium PP lol. I don't even want to think about the mass transfer of a 3 temperature/space engine like that.

I'm glad you put some solid numbers down on compression ratio vs. volume ratio now, as they get conflated even in some white papers.

I'm been in the hot PP camp forever and I was always baffled by cold PP until now.


Another 300-600k graphic, but where Essex DP/PP=4 vs Stirling DP/PP=8. I used 'megabar' P so everyone could follow m values easily. Again, Stirling DPvol and m is 2x Essex DPvol and m, yet both have equal output and PPvol. I think we can safely conclude that this Qin "anomaly" is solely related to the thermal ratio and that any cold PP will require greater Qin than equal hot PP proportional to the thermal ratio, regardless of actual DPvol/PPvol ratio. So, for now, I'll consider this simply a cold PP "tax" removed from other volumetric issues like compression and expansion ratios. Another nasty that can't be ignored is that for equal work, the greater relative Stirling DPvol will have more regen per cycle than Essex.

An amusing sidebar in above graphic is relatively high MEP since the expansion ratio is mere 1.25 (in both). Note Essex 3-4 where 2m transfer from DP to PP means 10m goes thru regen each cycle, but only 2m goes thru PP each cycle. This 5x factor would increase regen heat from maybe 2x ideal isothermal Qin (during expansion) to 10x factor that becomes even nastier when we factor this 300-600k cycle requires Qout during compression ~1/2 Qin during expansion, whereby total regen "load" could be 20x Wnet. Yeah, another numbers game, and when regen eff shrinks to realistic regen=.95 then this cascades thru cycle and shrinks total ideal eff=.5 to real eff=.25 in a flash.

Vincent - note paltry 1.25 expansion ratio is 2x compression ratio.

When efficiency is not important, the larger displacer volumes look impressive as they approach constant volume.

Matt, how about Essex Dp/Pp = .25 300k-900k? Sounds crazy but imo we can get very close real world.

VincentG wrote: ↑Fri Sep 20, 2024 6:45 pm When efficiency is not important, the larger displacer volumes look impressive as they approach constant volume.

Matt, how about Essex Dp/Pp = .25 300k-900k? Sounds crazy but imo we can get very close real world.

I guess you mean PP/DP=4 which leads us to this...

Here's a comp between gamma vs beta style DP shown as Essex scheme on left of graphic. As noted, upper graphic has distinct gamma style DP vs lower graphic has beta style DP. The gamma version represents DP=1 and PP=4 and I used a moving regen inside DP to simplify heat issues, however, real Qin would remain a challenge due to DP and piston sweep. This is merely to show effect of expansion Wpos vs compression Wneg which varies by cold volume. The point is mainly that the small DP vol in gamma version increases compression Wneg vs beta version and that both lack any 'cold stroke' akin common cold gamma. This clearly shows that terms such as "dead volume" can be fuzzy and vary by design. So, the whole design process starts with PVT values and often runs in circles between competing issues. BTW this 300-600k was recycled from another post and I was too lazy to fluff it into 300-900k cycle, but the more we compare hot PP, the more we'll find that the Rider is hard to beat due to simplicity. Yes, the Rider has inherent compression ratio limits (like most ECE), but the juggernaut of getting heat into any ECE remains paramount and moreso for any hot PP scheme.

The graphic on right was with this previous Essex graphic. This is a slight mod of my ancient "slingshot" scheme where 2 pistons chase each other in the same cylinder. I've posted it before and noted original scheme was for 'alpha' or Otto cycle with heat source at one end and heat sink at other end (regen between when alpha). The basic scheme is simple variable volume from continuous motion, but this can be gamed various ways such as 2 such cylinders cross-coupled or by adding volume behind one or both pistons (ie keeping all volume with a single cylinder vs multiple cylinders). So, in this graphic, I merely converted one positive displacement piston into a displacer, but kept the same 'piston' geometry, whereby a new bugger emerges.

Despite the displacer chasing the piston taxes pressure during expansion, note that the 4 bar isobaric expansion and the 1 bar isobaric compression both have 45deg durations. Now, note that Wpos and Wneg between these isobaric processes are equal, whereby the work balance for this 300-600k cycle is 4 bar Wpos for 45deg vs 1 bar Wneg for 45deg. Hmmm, a 4x pressure ratio from a 2x thermal ratio which leaves me wondering...

Here's an update on my gamma Cp regen loss theory...


Upper part of graphic is previous 300-600k gamma where DP/PP=2 whereby this 300cc PP has Wpos equal similar Essex where DP/PP=1

Lower part of graphic is where I unbundle values during expansion and compare upper 3-4 expansion via lower 3-3.5-4 expansion AND compression. The values under lower graphic reflect distinct events vs typical indistinct events, whereby if we consider 3-3.5 as an isothermal expansion followed by 3.5-4 as an isobaric compression then everything is nearly hunky-dory on energy balance. The only problem remaining is in the callout window where the black values don't jibe with anticipated red values. Note the black values -90 Win and +315 Qout where 315-90=225 and 225 is the Cv regen heat for 1/2 DP mass (my esoteric 6m here). However, isothermal Qin per each 1/2 of DP mass is 125. I took these values from an online calculator and quickly saw an evolving issue...I need the red values for everything to jibe via -90(ln 4) = -125. RA (ratio analysis) has limitations, but allows insight often missed by calcs. BTW ln4=1.386 and this bugger creeps into thermo often, so I'm left pondering what I botched.

Note some other tidbits amongst values, especially ideal regen=450 vs ideal input=250 whereby ideal regen load=1.8 and if this 300-600k cycle had Qin/Qout=.50 via Carnot then regen load=3.6x Wnet. My Cp regen loss theory for this example is not only that Wnet is reduced by 2, but also that regen load increased by 2 whereby for this example regen load=7.2x Wnet. This type of numbers gaming explains why SE solutions are lacking...

matt brown wrote: ↑Sat Aug 17, 2024 8:03 pm I've mentioned several times that any 600k expansion has only 2x work of same 300k expansion and nobody commented. The point to remember is that this is proportional expansion when isothermal such that ANY 1:2 600k expansion has 'only' 2x the work of ANY 1:2 300k expansion, so a 600k 100-200cc expansion has only 2x work of 300k 100-200cc expansion or 300k 500-1000cc expansion.

Very misleading, so consider this wrong, but my correction is more outrageous. My original 300k vs 600k comparison was to elude that a 600k expansion does not produce that much more power than a 300k expansion when engines "are equal". However, PVT values were grossly inadequate for this claim which should be that...

Any 100-200cc isothermal expansion has equal heat input and work output when pressure values are equal, regardless of temperature. Or a 300k 100-200cc isothermal expansion has Qin and Wout equal a 600k 100-200cc isothermal expansion when pressure values are equal. Thus, 10bar>>>1 bar 300k freebie ambient isothermal expansion from common shop air compressor produces work equal 10bar>>>1bar 600k frying hot isothermal expansion from fancy engine heater.

Kinda reminds me of: "God created man, Samuel Colt made them equal".

.

All those numbers require thinking. Its hurting my brain.

Ah 10 bars traveled to >>> 1 bar to go. Freebies! Probably should have someone else come get me and drive me home.

Samuel Colt made them equal. Jack Daniels made them not care. LOL

Sorry Matt it's only work if expanded in an engine. Free expansion, JT effect, zero work. Irreversible.

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