Stirlingengineforum.com

Along the lines of Mark Twain's quip about the weather where "everybody talks about it, but nobody does anything about it", I see tons of regen hash, but nothing about how much heat regen entails. Kinda lame, don't you think, obsessing over an unknown quantity ??? Consider a common Stirling cycle where Tr=Pr=Vr =2, aka a sq cycle wherein Tr=2 means ideal eff=.50 regardless if monatomic (Ar) or diatomic (air). Offhand, the only other thing we know about this 'sq cycle' is that P after compression = P after expansion. Again, assuming an ideal cycle (with ideal gas) we know that if Qin=1, then Qout=.5 and Wnet=.5, but what is Qreg (regen) and what is Qreg:Qin ? No doubt, ideal Qin/out/reg & W will vary by m (n, mols, atms, whatever you want to call contained gas mass) but the (ideal) ratio Qreg:Qin will remain constant despite m variables except for monatomic & diatomic variables.

I suspect that Nobody knows this (wink-wink) and that since dU is constant between isotherms (internal energy is constant between isotherms regardless how long isotherms appear on PV plot) and that the long banner like PV plot of LTD (~Vr/Tr>6 aka relative compression ratio exceeding 6) has worthless regen vs flag like PV plot of sq cycle (above).

This is first principle stuff, and Elon Musk often uses this buzz.

Matt,

An intriguing question.

I'm not sure I follow the meaning of Tr, Pr and Vr in the context of your question as those are more commonly encountered as the reduced standard variables in Equations of State. The thing I'm hinting at is that an Equation of State is a steady state affair that doesn't address changes of state such as converting a quantity of heat to a quantity of work which is removed from the (closed state) system. And, as you say, we don't use Ideal Gas as it seems to be in short supply!

Anyway, that aside, there is indeed a lot of "regen hash" as you put it. Meaning..... I don't think anyone knows.

Some of the "regenerator hash" says that the regenerator must have a thermal gradient across it, and this does seem plausible (to me), making the meaning of Qreg a bit tricky to fathom as it can't be uniformly distributed across the regenerator matrix. Which, to accompany the Mark Twain reference, is a bit like Anne Elk's Brontosaurus Theory (Monty Python) - it being thin at one end, much, much thicker in the middle and thin at the other end.

Understanding history explains many mysteries, and a walk thru thermo history has Watt using his 'indicator' diagrams decades before Clapeyron used crude PV plots shortly after Carnot's death. During most of the 19th century, the caloric theory reigned, and even after Joule's concluding what the mechanical equivalence of heat was in the late 1870s, the kinetic theory was only slowly accepted. Thermo's big event was also in the late 1870's when Otto discovered the compression cycle while messing with an Otto-Langen eng, the eureka moment for Otto and eng history. Grasping what these early guys were doing is boring history to most, but explains much thermo hash by those that don't know.

After Otto, engs became credible, and interest exploded (cute pun). However, thermo study quickly focused on analysis over building (heads up everyone) and the tool of choice became the PV plot which was a good visual vs fuzzy calculus. Yep, the thing we call a PV plot became the dominant GA (graphical analysis) for decades, since it could both make you moola and save you moola. I'm a big believer in GA and it's little brother RA (ratio analysis) since RA is almost creepy sweet in thermo. OK, so I'm really into PV plots and various ratios, so previous Pr,Tr,Vr is nothing more than press ratio, temp ratio, and vol ratio.

A sq Stirling cycle has Pr=Tr=Vr, and very similar to most comm'l engs, but requires finite values to be assigned. An example might be Pr=Tr=Vr=2 where Pr=2 is 10 atm low press with 20 atm high press, and Tr=2 is 300k low temp with 600k high temp, and Vr=2 is 250cc low vol with 500cc high vol. Again, only one ex of Pr=Tr=Vr=2 and there's countless such values that one could assign to sq cycle=2, and countless such for other 'sq' cycles. It's merely a mental construct ripe for comparison/contrast with other cycles.

https://ibb.co/98Yq7Vk

Alphax - attached pic shows various 'heat' calcs, but ignores quantifying regen heat. This common exclusion is the sucker bait for Stirling treehuggers and grant meisters. Quantifying this value for any cycle, and comparing it as a ratio to other heat values within a given cycle, will likely nix your ECE hobby. Simply gaming PVT values is lame, and explains most layman failures. Please ignore the word 'ideal' in this pic, but if points 1 & 3 had equal P than this would be an ex of a sq cycle.

Yikes, I hate to sound so condemning, but millions of guys have wasted much of their lives chasing this Holy Grail with little to show for it. 20 yrs ago, when I told James Senft that Walker's first book is was got me into SE, he replied, "that was also the book that did me in". No, I haven't given up on the chase, but I do approach stuff slower (like walking thru a minefield).

Permit me to pull the curtain back on regen heat...

Looking at this pic, thermo guys should instantly know several things beyond stg 1 is isochoric, stg 2 is isothermal, and stg 3 is isobaric. IOW stg 1 will 'involve' Cv and stg 3 will 'involve' Cp. So, for an ideal diatomic gas (similar air) we know that Cv=5/2R and Cp=7/2R, or least this is what the brainiacs tell us (gotta have some humor). However, we also know some other things, since this is another 'sq' cycle (3 legged flavor) where Pr=Vr=Tr, and if we consider Pr=Vr=Tr=2 with T1=300k at P1V1 then T2 at P2V1=600K, since dP is linear dT when isochoric. Now, playing with the xlnt "combined gas law calculator" at

https://www.omnicalculator.com/physics/ ... -processes

(scroll down and select this particular option) I ran some simple values thru and came up with some nice round numbers in Joules wherein the heat ratios per process were a simple visual. Merely dividing by 1000J, the ratio was stg 1=5, and stg 3=7, while stg 2 =2.77 so it appears the brainiacs are right.

And for an ideal monatomic gas (similar argon) stg 1=3 and stg 3=5, and stg 2=2.77 (note no change stg 2 mono vs dia).

Consider attached PV a sq cycle where V2 would be reduced slightly such that P at point 2 equals P at point 4. This returns us to another sq cycle, and many comm'l SE hover around sq cycles, tho different widely within this 'class'. So, consider this another sq cycle (4 legged flavor) wherein Pr=Vr=Tr=2, such that previous 'heat triangle' was the 'upper half' of this PV plot. Let's recycle the same values, such that (I'm going to use the mismatched points per this plot) pt 4=300K and pt 1=600K. We already know from the previous heat triangle that if input Q=5 during isochoric process 4-1 (here) then Q=2.77 during isothermal expansion process 1-2. And we know (or should know) that since there's no change in internal energy for an isothermal process (dU=0) then ideal regen process 2-3 will (also) have Q=5. Now, if we fudge that isothermal input Q=2.77 just a tad to Q=2.8, we'd find...

heat input 2.8
heat output 1.4
work output 1.4
ideal regen 5

OK, are you guys onboard with how you game this stuff ??? Note that for THIS cycle with one fall from ideal grace where everything remains ideal except for regen, regen=.8 would 'tax' this system 1 unit of add'l heat vs only Wnet=1.4 units !

Yep, regen cycles are not for the faint of heart, and the devil is in the details. No, alphax, lots of guys know this, they just keep it secret (would nix their grant schmooze). I'll leave it as extra credit (lol) for those who wonder about same cycle but monatomic (merely sub in mono Cv & Cp) and discover how same .8 regen gets a break (mono vs dia). I'm big on GA & RA...

Again, don't get me wrong, I'm still in the chase, but to quote Twain "I never let my schoolin' interfere with my education."

Just to cover my butt (but doubt an issue here) if anyone reduces dia values whereby Cv=2.5 and Cp=3.5, and then reduces my input Q=2.8 likewise to Q=1.4, this has nothing to do with dia gamma (Cp/Cv) and merely a coincidence. Gadz, that caught my eye like a big dog...

Hey Matt, I suppose you could call this stirring the pot, but I can’t resist and I hope you take it in fun. This thread reminds me of the book “Air Engines” by Theodor Finkelstein and Allan Organ, wherein Organ goes on and on about “The regenerator problem.” It’s evidently very useful for folks who like to fill up chalkboards and notebook pages with symbols and numbers and charts and graphs, and Organ seemed to fall firmly into that camp. What struck me funny was that in the next section he laid out how Stirling hadn’t just struck it lucky, but had actually solved problems logically, before all of the smart folks came up with all of the symbols and numbers and charts and graphs. Yeah I admit that a lot of useful science had already been done before 1812, but the funniest part was when in explaining Stirling’s success, Organ states: “It is worth considering also that (Stirling) had a head start on a number of counts: he would not for example, have been aware of the distractions the mathematicians were to inflict on regenerator theory.”

Bumpkin

Greetings Bumpkin - I'm reminded of a physicist who told me yrs ago that his favorite thing in science was the kinetic theory since it even explains why the soup gets hot, faster, when...stirring the pot (disturbs boundary layer). Although I've been chasing this Holy Grail for yrs (decades), I always try to take it with a ton of humor, otherwise I'd go nuts.

My backstory - I got into SE during the early '70s while still in high school. Like many thermo guys, my childhood hero was Watt who simply slapped a condenser on a steam engine, and changed history...no rocket science req'd. At the time, I lived in Calif. (bummer, still do) and the first Green Movement had everyone clamoring to nix ICE, except gearheads like my older brother (steam was my refuge during sibling rivalry). I stumbled into single phase gas via Carnot, but I was too young to understand all the calculus mumbo-jumbo, and this lack of thermo 'accessibility' haunted me for yrs. Ultimately, my thermo 'access' came from carefully retracing thermo history, but this took yrs, since all BC (before computers). My early steam interest found comfort in relating gas cycles via PV plots, but I found the endless calculus fuzzy (not intuitive), so I sought to extend early thermo via RA (ratio analysis). This works great, and likely our future thermo edu ('classic' thermo has been stuck in a rut since the atomic theory gained prominence - 'thanks' Al).

I have most of the well known 'Stirling' books, but they just sit on a shelf. My copy of Air Engines is like new, since I only flicked thru it once and thought: great, more mumbo-jumbo. Years ago, OPEC had a large think tank watching for any Big Oil threat, so they could get in early. As I recall, after about a decade, OPEC stopped funding, secure nothing was forthcoming. So, the Saudis alone took over funding, albeit reducing staff, and their 'readers' remain convinced that academia poses no threat. No, they're looking for some guy in his garage, working alone, that will stumble across the next great thing...

I spent yrs trying to quantify regen into something similar Carnot eff equation, and shocked that even the living legends (Senft, Urieli, etc) appeared clueless. I eventually got it from the heat triangle in this thread (eyes roll) and suspect this sank yahoo's 2 big energy groups in early 2000s (1000s of members with many engineers, profs, and some physicists). Yep, quantifying regen in simple terms exposes just how top heavy regen cycles are, and once one realizes that for any powerful cycle (approaching sq cycle vs LTD stuff) that the ideal heat of regen will be multiples of ideal input, then a parallel to Rankine Cycle appears wherein boiler dwarfs engine, Stirling regen dwarfs input. Once you get your head around precise Qregen/Qinput (as simple ratios) you can spend days pondering the fall from grace as even the most ideal cycle succumbs to various mech realities. Most guys will never know this ratio, and think that it's meaningless. But, these same guys will attempt the impossible until the old lady's on their back or fresh grant moola fails to appear. Then they wander away, just another walk thru in a nearly endless stream of dreamers and conmen.

Yep, Stirling got lucky, but moreso Otto. Meanwhile, Dean Kamen has gotten nowhere due to still 'chasing windmills' via computer sims where: garbage in = garbage out. When gov't took over edu, science became a master:slave issue where teachers are gatekeepers to maintain the status quo (or 'increase' the status quo thru greater inequality).

Yep.

@ Nobody

Thanks for the 'peer review'. Now, do you see how vol ratio effects eff ??? where increasing vol ratio within other cycle constants increases cycle eff. The major issues would be (1) scheming suitable mech, and (2) solving regen pressure drop between blows.

Once you see that high temperature Stirlings are sorta useless anyway, it’s kinda liberating when you realize that dead space isn’t, as a percentage, as important to low or moderate temperature engines as to high temp versions. It lets you shift the compromises towards more flow or more regeneration if you want. Kinda like Stirling’s first engine; it had a lot of regenerator, but with the high volume ratio of its mid-temp design there wasn’t really much dead-space penalty. No, Stirling wasn’t lucky; he was logical.
Bumpkin