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Ultra-pressure engine efficiency

Posted by Tim Nye 
Re: Ultra-pressure engine efficiency
February 10, 2015 06:15PM
Most of the calculations in this thread are just to darn simplified.

Only a full on simulation including heat transfer is going to get accurate results.

The steam expansion modeling is only a first step. Heat transfer on mass transfer modeling must also be applied. Then rpm is involved.

With each refinement we can get better results be for wasting expensive build resources.

We need an instrumented test engine to check the mathematicAL model against.
Re: Ultra-pressure engine efficiency
February 10, 2015 06:39PM

That is exactly what the late Professor Hall did. He also included valve flow losses. The heat transfer is simplified via the entire cylinder, head and piston assumed to be the same temperature and the program is limited to the Walschearts valve gear. It also doesn't include the flow losses in the steam channels, just through the valve ports themselves. It could be much more detailed. He outlined the formulas he used for the program. I have linked to those papers in the past.

He compared the program to a single cylinder test engine and various locomotive indicator cards taken at speed, he used this to fine tune his program. I think his work is possibly the most undervalued

When he was alive he provided people with the code for his program, I am not a programmer so I never bothered to get it, don't know if anyone has it. The program is available though, as I have linked to before.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
February 10, 2015 09:43PM
I think a good test engine could somehow be considered a well programed analog computer. Just a muse.

Anyway, I believe ultra pressure would best be used as a first stage in a compound engine. In mine the first stage expansion ratio is only around 3:1. Super critical steam at 850 deg F to 1,200 deg F is expanded to 1,100 psia. This in a counterflow configuration which at the high exhaust pressure is smaller displacement than a uniflow configuration. Zero clearance, zero compression. (Thanks Jerry)

This high pressure counterflow exhausts into an exhaust line going into the Lamont tank. Lamont tank water is sprayed into this exhaust line like a normalizer and brings the conditions down to saturated steam at 1,100 psia plus excess water. Steam is generated by this process at from 10% to 30% extra. Steam from the Lamont generator is then added, if needed and back to the superheater for use in the next two stages of the compound. If less steam is needed then the high pressure stage is throttled or it's cutoff increased. This gives control of the difference in steam usage between the first stage with re-heat and the next two stages. This first stage is tailored in size so the engine is operating at maximum efficiency where it is needed, which generally is not full throttle. Now we have re-heat in a car.

Have fun playing with it.


Bill G.
Re: Ultra-pressure engine efficiency
February 10, 2015 10:45PM
Hey Bill,

"I think a good test engine could somehow be considered a well programmed analog computer. Just a muse."

You are precisely correct.

My own adaption of Professor Halls program, mine in spreadsheet form and assuredly flawed in numerous ways, calculates the engine with ten steps per degree of crankshaft rotation. One crude way to determine the relative accuracy of such a program is how "analog" the charts look. Really one must look much deeper and analyze very critically. At one point I had it doing 100 steps per degree of rotation and I couldn't do it all in one set of columns for each side of the piston, so I had to break it up into two pairs, 18,000 rows of calculations per pair, it didn't give data or outputs that were more precise or "analog" looking. So back to 3,600 rows of calculations for a complete revolution, two pairs of them, one for the head end, one for the crank end.

From my perspective the future of light steam power lives in the application of finite element analysis on a holistic scale.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
February 11, 2015 01:53PM

My friend, Ron henry, is the guy who invented the spread sheet. Back when he worked for Control Data.



Bill G.
Re: Ultra-pressure engine efficiency
February 12, 2015 09:35PM
Wild stuff Bill.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
March 08, 2015 02:53PM
Jerry, The problem with your cutoff is that cutoff is valve timming. It could be in degrees or stroke percent. I agree that volume ratio is what one needs to use in calculations of expansion ratio. It is just confusion to use a different definition of cutoff than what has been used for so many many years. Clearance volume is a parameter in calculating expansion and compression ratio. It might even be variable Independent of inlet valve opening and closing. Inlet can open before TDC.

Sorry Just got confused on you posts again. Forgot how you use cutoff.


Edited 1 time(s). Last edit at 03/10/2015 01:05AM by steamerandy.
Re: Ultra-pressure engine efficiency
March 11, 2015 09:08AM

I think the genesis of any confusion over the proper definition of cutoff resulted from many early 1900's authors who had the preconceived notion that clearance had no effect or very little effect on economic performance. Some authors went so far as to claim that the only effect of clearance was to cushion the piston as it passed TDC. Yet, a few others did recognize the benefit of high compression operation (HCO). As a matter of convenience, the definition of cutoff (and clearance) in many texts was based on piston displacement. This mind set was challenged in 1946 with the introduction of the Williams cycle.

To properly represent the true number of expansions and the impact that clearance has on performance, the cylinder volume at cutoff must include the clearance volume. Likewise, at release, the cylinder volume must include the clearance volume.

Confusion arises when one tries to apply the teaching of an old text to explain advantages of HCO. Now, after years of debate and accumulation of analytical data, the Steam Nation generally accepts the fact that a valid representation of cutoff and clearance must be based on the absolute cylinder volumes that participate in the admission and expansion cycle.

While much can be said about the thermodynamics of HCO, the reason that the Williams Cycle offers an advantage is because it behaves as an engine having an effective zero clearance. Now, consider an engine have a quasi-zero clearance without the baggage of compression work. This is known as the z-cycle and it will add an honest four (4) percentage points to efficiency beyond that offered by HCO.

Re: Ultra-pressure engine efficiency
March 11, 2015 07:56PM
Hi Jerry,

I really don't see where the Williamses invented anything significant, certainly not a new cycle. Their engine was uniflow...that patent goes back to the mid 19th century. The valve that vents over-compression back to the steam chest...that was also patented about then. Recompression of steam? Some patent literature, again in the 1800s, discusses the benefits. Stumpf makes the entire topic clear in his two books. I don't believe any evidence exists that the Williams engine was the functional equivalent of zero clearance. Stumpf discusses clearance in great detail years before the Williams patents touch on it sketchily. Stumpf is very clear in stating that the "bad effects" of clearance are reduced, but not canceled, by recompression. His work includes extensive mathematical proofs AND indicator cards, graphs, tables and other data derived from tests of industrial engines based on his work. The Williams brothers never supplied any proof of their claims and some of those claims are mathematically suspect. Even the concept of zero clearance is hardly new, Stumpf mentions the idea in his book and acknowledges improved economy. Engineering texts before 1910 certainly include clearance volume in their calculations, it wasn't an obscure idea.

I don't mean to be contentious, but the Williams brothers have been given credit for the work of many others. Their claims for the efficiency of their engines is very suspect and lacking in proof. Much of what is being claimed as relatively new was well understood over 100 years ago, recognizing this gives us a better historical perspective on the technology.


Re: Ultra-pressure engine efficiency
March 12, 2015 12:12PM
Thank you Ken, you are quite right, the Williams didn't invent anything that was new.
Back when all this huffing and puffing was going on, the exact same conclusions were made in the drafting room at Beslers, people reinventing things that were a hundred years old.
Similar today to the goings on at Delusions-Are-Us.
Re: Ultra-pressure engine efficiency
March 13, 2015 08:25AM

I was responding to Andy's inquiry about how I use the definition of cutoff in my analyses. Andy prefers to define cutoff based on piston displacement per many old texts. My argument to Andy is the fact that, unless cutoff and clearance are based on absolute volumes, there is no chance that the calculations will represent the true number of expansions, let alone present a valid assessment of high compression operation.

What assumptions about cutoff and clearance have you applied to your analyses of the Williams Cycle? Also, does your analysis include the mixing effects of the characteristic mass (residual steam mass) with the admission mass? Just as important, do you make a temperature correction to the admission mass within the absolute volume at cutoff? In your analysis, do you assume that expansion ends at release or at BDC? If you assume BDC, what portion of the "toe work" represents the total? And finally, does your analysis include a frictional model that limits all possibility of a complete expansion? Please consider these items as rhetorical questions.

The point is that much more attention must be paid to analyses of HCO than that associated with a conventional Rankine Cycle.. While the Mollier diagram will capture the essences of energy conversion of heat engines, any cutoff at large cannot be duplicated on the Mollier diagram for any arbitrary choice of supply pressure and temperature. There re no absolute volumes associated with the Mollier diagram. Unless your analyses captures the optimum value of cutoff, the full potential of HCO cannot be realized. Keep in mind that the Mollier diagram is no more than a graphical representation of the properties of water.

Re: Ultra-pressure engine efficiency
March 13, 2015 11:28AM
Jerry, cutoff is a mechanical valve timming. We can, a day have used cutoff in degrees of crank rotation. Cutoff is valve open time. It is nothe volume. That is how it is used in all those old books. With cutoff as percent of stroke and clearance as percent of displacement. As is common. IC engines include clearance volume in figuring expansion and compression ratios. Valve timing are not changed to include clearance volume. I have a thermodynamics book from 1935. It talks about the inclusion of clearance in figuring expansion ratio. It does not change the definition of clearance as the point at which the inlet closes. Cutoff is the point at which the valve cuts off steam addmission. Valve timming.

The Williams engine from my understanding had variable clearance . Vc Volume at cutoff. Cutoff as in cutoff valve. It common usage that cutoff applies to a valve. Or a point. Cutoff point. We say we have a cutoff point to get something delevered. A point in time.

because I use cutoff as point in stroke % does not exclude clearance which is a percent of displacement.

Expansions = (clearance + displacement)/(clearance + cutoff)

It is also well explained that the ideal Rankin cycle does not include clearance in those books. Clearance when used is usually in percent of displacement.

The ideal zero clearance cycle is a reference cycle that a real engine is messured against. And is still used in the same way.

No big thing. I forget you are from another planet or something and use a different language.

Re: Ultra-pressure engine efficiency
April 19, 2015 08:05PM
It's like which way does electrical current flow; the definitions (wordings) may not make perfect sense all the time, but as long as we are consistent, we can share our book-keeping effort without unnecessary confusion.

Andy, I believe your definitions above is consistent with the overwhelming majority of what I've read.
I have a small contention though:
"Expansions = (clearance + displacement)/(clearance + cutoff)"
So you are saying, an unaflow with release at 15% and one with release at 85%, they have the same number of expansions?
Because, displacement includes the volume swept after release, of this I am pretty sure.

Is it not more correct to say something like
"Expansions = (clearance + release)/(clearance + cutoff)"
which is the same as
"Expansions = (maximum enclosed volume)/(volume at cutoff)"

Or is your above definition of expansions one that is widely used? That would be confusing!
Re: Ultra-pressure engine efficiency
April 25, 2015 03:30PM
I agree that release has to be part of the equations.

The ideal cycle does not include time. Actual release and admission are dynamic. Inlet may open befor TDC and release before BDC in any engine. Counter flow engines may open exhaust before end of stroke. In a static cycle having compression it might be simpler to not include the the uniflow exhaust open volume in its displacement sense in a static cycle an instainious drop to exhaust pressure is the norm. A static cycle is vary idealized. The ideal cycle is vary simplified. I agree with Jerry in principal. But the redefining of terminology is what I take exception with. You find in many scientific and engineering fields simplified formula. When highly spicific formula are used the terms of the simplified versions are not redefined. Others are added. It is just not the way it's done. We need consistent terminology in order to communicate ideas. Cutoff is the point at which inlet is turminated. It is a timing point relating to piston position. It also can be in degrees of crank rotation. Several books I have have diagrams that show actual engine timing where cutoff is in degrees. And I think release was also shown in degrees as well.

I do not think it complicated to include clearance in the calculations. Clearance is an important design parameter. it effects compression and expansion. The Williams engine had variable clearance. Changing clearance did change engine displacement. In that case it comicates the the analysis of the engine. Clearance could be changed by varying the engine stroke. The displacement would also chang. I can not see how it helps analysis to combine independent parameters.

How hard is it to include clearance in calculating expansions.

expansion = (clearance + release)÷(clearace+cutoff)

cutoff = (clearance+release)÷expansion-clearance

In design it is important to be able to figure a cutoff given a desired expansion ratio.

Don't get me wrong. Jerry is very smart and make valuable contributions.

Clearance is nor a new parameter. It is in my oldest books that were first published in 1936. The talks about it effect on expansion ratio. But in calculation of the ideal cycle it was intentionally ignored. The ideal engine is the best the cycle can perform and is compared to real engines to get engine efficiency. The ideal full expansion cycle is the turbine cycle. The partial expansion cycle reflects the ideal piston expander.

It's not that big a deal except me being forgetful and we go several rounds figuring what we are talking about.

Re: Ultra-pressure engine efficiency
April 25, 2015 04:08PM
Williams had variable compression thanks to that compression relief valve between the cylinder and the valve inlet chamber.
If they actually had variable clearance, which infers a variable stroke or clearance volume, how did they do it?
Piston quad expansion expanders have gone to 27" vacuum on the LP exhaust, as good as any turbine can get. So what's the difference?
Re: Ultra-pressure engine efficiency
April 25, 2015 04:58PM

If they actually had variable clearance, which infers a variable stroke or clearance volume, how did they do it?
Re: Ultra-pressure engine efficiency
April 25, 2015 05:44PM
Do you know, because every photo I have seen of the Williams engines does not have any such mechanism? Only that automatic compression relief valve in the head.
Re: Ultra-pressure engine efficiency
April 25, 2015 10:59PM
Having looked at all the Williams patent literature and examining a few of their engines in Tom's shop, I have to say I have seen nothing that appears to lend a variable clearance capability --- no matter what else that check valve does, it closes and seals a fixed volume of steam in the top of the cylinder. The only patent for such a thing on a car engine that comes to mind at this late hour is one of the Jay Carter patents. While he obviously built the bump valve uniflow aspects of the engine, I don't think he constructed the variable clearance mechanism. As designed it probably would have been problematic --- and the rest of the hardware is pretty simple and straightforward --- I figure this was meant to keep the possibility open if the development work went further.
Re: Ultra-pressure engine efficiency
April 26, 2015 09:50AM

The Williams engine I know of had a movable piston in the headad that separated the steam chest from the expansion chamber. Not sure where it was I saw it. Maybe a post here or in a paper on the engine. I think it was from the patent redrawing. It has been a long time sense I saw iit. It didn't have a pressure release valve but an auxiliary exhaust valve the was manually engaged. It may have been advertising. It's been 10 to 15 years sense I looked into the Williams engine.

You mentioned variable stroke. How many do you know of besides me? We're they trying to achieve variable compression or just displacement. I have only found designs that vary displacement trying to keep TDC volume change to a minimum. Most are pumps not engines.

A wobble plate or swash plate engine can achieve variable stroke but doesn't look all that strong. They also would present balancing issues. Many IC designs have been attempted some wit small soccess. Most were early aircraft engines. Still used in many pump designs.


Edited 1 time(s). Last edit at 04/26/2015 10:30AM by steamerandy.
Re: Ultra-pressure engine efficiency
April 26, 2015 01:05PM
My suspicion is the Williams patented variable clearance just to protect the idea; but never built one.
Roy Renner when he was there looked for it, on our list of things to verify; but reported he never saw it.
My thought was that it got just too complicated and they used that automatic compression relief valve in the head along with a high compression ratio instead. There was just too much secrecy and unverified claims surrounding the Williams to take anything they said at face value. Like from Florida now.
Ken raises a good point. Just how much steam is compressed in the inlet valve chamber volume and does it really do all that much good? Minimal clearance and a secondary exhaust valve in a unaflow engine makes a lot more sense to me.

Wobble plates, Z cranks and cam engines have all been successfully built. Swash plate can have slipper bearing lube problems. The wobble plate and Z crank can be drilled for pressure lube. SAAB used one of these in their steamer. What happened to that Gibbs-Hosick engine they built?
That Hermann cam engine passed the FAA tests and was certified for flight. Stanford University had a running one in the engineering lab.
I used to be interested in the wobble plate just because it was compact; but then the Wankel arrived and that won out as far as i am concerned. Also removed any lingering thoughts about rotary inlet valves. UGH!!

Edited 1 time(s). Last edit at 04/26/2015 01:08PM by Jim Crank.
Re: Ultra-pressure engine efficiency
April 26, 2015 02:36PM
Hi Jim

That cam engine Gibbs conversion still exists in IC form. Changed hands.

This engine, s-ram, is intersting. Looks like it transfer stright line motion by putting the sliding motion in the rode joint. Also putting the connection offcenter of the wobble plain to control clearance change to stroke change is interesting. Watch the animation.

Re: Ultra-pressure engine efficiency
April 26, 2015 03:11PM
Hi Andy,
Someone converted that Gibbs-Hosek steam engine to IC. Why???

OK, the web site is interesting and needs study. Basically it seems to be similar in motion and operation to a Z crank; but with a variable stroke.
There are still a few things that would bother me if it was used as a high pressure and powerful steam engine. The load contact points are small, oscillate and would see a very high loading, a problem with all these barrel engines. The balance issue with only a few cylinders needs analysis. The obvious easy use of a rotary valve is there and that is not good at all, so a cam operated poppet valve system would be cramped and difficult. I see their patent attorney got rich off this one, they usually do.
Will look further; but after forty years working with a lot of Wankels, I still prefer that one as a steam engine.
Re: Ultra-pressure engine efficiency
April 26, 2015 04:05PM
I believe the aforementioned Williams engine is embodied in US Patent # 2,402,699 simply entitled "Steam Engine". Figure 10 does indeed show a variable clearance volume, my mistake.

However, this volume is not a part of normal operations and is offered as an optional item. The admission valve cutoff is actuated by steam pressure and the variable clearance is provided so that "the closing of the steam valve or valves, as the case may be, will be delayed when the engine is started and picking up speed while, after the engine has gained speed, the piston may adjusted for decreasing the effective volume of said chamber and advancing the closing of the valve or valves to thus economize feed steam." Note that efficiency is credited to "advancing the closing of the valves" and not to the clearance volume itself.

The patent clearly states "A further object of the invention is to provide a large clearance volume of steam of a compression pressure not greater than the operating pressure of the feed steam but of higher compression temperature".

Curiously, the Williams refer to large clearance volumes in regards to providing high efficiency. I am sure Stumpf would have some questions.

The patent goes on to imply that efficiency is achieved by higher temperature compression steam mixing with the lower temperature admission steam to create a higher temperature mix; this higher temperature raising efficiency. I can't find anything in Stumpf that validates this conclusion and my own math tends to find that the higher mixing temperature has no real benefit thermodynamically, any benefit is absorbed in the work of compression. As Stumpf would note, the advantage is that the compression progressively heats the piston and cylinder wall as the pressure rises so that the admission end of the cylinder wall is kept warmer than the exhaust belt; reducing heat transfer to the cylinder from the steam.

Much has been made of the so-called "Williams Cycle" and the wonderful thermodynamic benefits. This patent has always made me question just how well they did understand the Rankine Cycle.


Edited 2 time(s). Last edit at 04/26/2015 04:08PM by frustrated.
Re: Ultra-pressure engine efficiency
April 26, 2015 04:33PM
One of the things that bothers me (and maybe I haven't researched this to the proper extent) is that the Williams operation made claims about how the intake charge of steam increased the superheat in the intake steam because of the recompression of the residual steam in the cylinder which was bypassed back out due to excessive recompression.

IMO this would imply "reverse" adiabatic calculations, and resulting graphs. Most of the adiabatic calcs are for expansion--and I assume that simple reversal of these don't satisfy the need for accuracy here. Has anyone tried to perform "adiabatic compression" calcs to see if there's any possibility of duplicating the Williams' claim?

I suspect our fabulous engineer (and current Prez--thanx!) may have much more succinct comments-a-vouz here.

All comments invited as usual.

Bill H.

Edited 1 time(s). Last edit at 04/26/2015 06:05PM by Bill Hinote.
Re: Ultra-pressure engine efficiency
April 26, 2015 05:14PM
Hi Bill,

Compression to higher than inlet temperature is no big deal. The same formulas work in expansion and compression. The compression and expansion are closer to "isentropic" than anything else. If you look at old patents (Bruno Nordberg among others comes to mind) there are mentions of compression to above admission temperature. It's simply a matter of having a higher compression ratio than expansion ratio, given the mere fact of cutoff it is almost certain that will happen. Whether the compression ratio is ENOUGH higher is where the math begins. In any case, observations of compression to higher than admission temperatures was noted by the late 19th century, as I recall. I don't belive there were any serious claims that the mixing temperature raised efficiency until the Williamses came along and, as so often happens, we're still awaiting proof.


Re: Ultra-pressure engine efficiency
April 26, 2015 06:39PM

Due to the increase in entropy the "closeness" to isentropic expansion and compression will raise the re-compression temperature. A decent, clean expansion will still see some increase in entropy due to turbulence, wire drawing as the inlet valve closes and such. The resultant exhaust temperature is then higher than the expansion ratio would indicate. The residual steam is then starting re-compression at a higher entropy. There is then less work output than an "ideal" expansion would indicate and that work loss energy goes to increase the exhaust temperature. I am disregarding heat gains and losses to the cylinder here.

Starting then at a higher entropy than the expansion began at, the re-compression cycle will end up at a higher temperature than the inlet steam when re-compressed to the inlet steam pressure. Also, there is an increase in entropy in the re-compression cycle which will further add to the temperature increase.

Both cycles; expansion and re-compression, have an inherent efficiency loss, not a large one but notable. In a turbine it is caused by blade efficiency losses.

As I understood it, the possible increase in engine efficiency by using the increase in "inlet charge" temperature caused by the re-compression, was only in the use of low superheat engines so as to stop any condensation problems during expansion. The mixing of a higher temperature quantity of inlet steam with a lower temperature inlet quantity is inherently counterproductive thermodynamically. Better to raise the superheat.

Ideally, re-compression to exactly the inlet pressure and temperature is best to help eliminate clearance volume losses. Even a Z cycle engine should have a little re-compression as a real zero clearance is not practical.

The ring pack should be pre-pressurized anyway, I think. I would try for one compression ring for a maximum of every 400 psi of inlet pressure. I don't think that over 400 psi on a compression ring is good practice, so the ring pack should have a good even pressure distribution before the inlet valve opens and slams over 1,000 psi on the top ring only. Re-compression to around inlet pressure would give the time element to do that.


Bill G.

Edited 1 time(s). Last edit at 04/28/2015 07:03PM by Bill Gatlin.
Re: Ultra-pressure engine efficiency
April 26, 2015 08:04PM
Sorry to go a bit off topic:
Perhaps one of you can help me find a paper I had on a special experimental opposed piston rocker two stroke diesel engine, much like the Commer TS.

It had a variable clearance:
The rockers pivoted on eccentric axles, with control arms on them. The control arms on each side was tied together with a threaded rod and a screwing mechanism.

I can't find that paper, it seemed pretty old, scanned PDF. If anyone knows what I'm talking about, let me know so I can find it again.
Re: Ultra-pressure engine efficiency
April 27, 2015 10:48PM
Hi Bill,

I did say "closer" to isentropic grinning smiley ; adiabatic expansion isn't nearly as good a model.

Recompression doesn't eliminate clearance losses although it does lessen them. Stumpf stated that and when I work the calculations out using a couple of different methods I get the same result. Since Stumpf actually tested a large number of engines to a high degree of accuracy, I certainly find his statement to be far more definitive than mine.

Likewise, I find that the Williams relief valve reduces losses compared to over compression but certainly doesn't eliminate them. Better to close either the exhaust valve (or an aux exhaust valve in the case of uniflows) at such a point as to produce recompression to about admission. This is simply done by adding a cam phaser from a modern automobile, the phase angle can be directly set by admission steam pressure. It isn't perfect since it assumes a known condenser pressure but it gets questionable whether adding more complication to tune the system in by that little degree is worth it.

I agree, compression heating may help lower temperature engines improve their efficiency by combatting initial condensation upon admission; this not so much because the heated compressed steam is mixing with the admission steam but because it has heated the cylinder walls during compression.

Truthfully, every time I work it out, higher recompression temperatures mixing with incoming steam simply add no thermal benefit to the system. I don't really find a loss, either. The mixing seems pretty neutral. I come out a bit above or below depending on conditions but I assume rounding errors may account for that given the relatively small differences.

One thing that tends to pop up is that overcompression might be better handled by a valve that dumps the excess pressure to an early point in the superheater rather than back to the steam chest. (I'm assuming the throttle valve is at the beginning of the superheater and the recompression is dumped in just downstream of the throttle). Pumping the recompression to the chest seems to mix higher entropy steam with the lower entropy incoming steam at a loss, mixing in the early part of the superheater causes all the steam to reach the same low entropy before hitting the cylinder. But adjusting compression onset to effect full recompression seems the ideal solution.


Re: Ultra-pressure engine efficiency
April 28, 2015 03:34PM

Compare mixing the mass of uncompressed, partial compression and full compression to inlet pressure.

In a static cycle the mix will be with them at equal pressure. Mass of residual steam compressed to inlet pressure and mixed with inlet steam. Compressing the residual would be combination the admitted steam mixing and cylinder volume change. There is always some energy loss in the process. What in trying to explain is the residual and inlet mix process resulting state would be deturmined the sum of their enthalpy normalized to the same pressure and mass. What process do we apply to the pressure change of the residual steam to inlet pressure. Ideally admission is at constant pressure. We have the residual steam in the clearance space, possibly at a lower pressure. On admission the pressure goes to inlet pressure. What process should be applied to the residue steam state change to admission pressure determining it's enthalpy?

The residual steam is the combination of the mix expanded and exhausted leaving some fraction of that mix, the residual part that is then mixed with the fresh admitted steam. My cycle calculator looped until the mixture at cutoff stabilized to some number of decmal places. The differance between the curent and previous enthalpy of the mix is less then curent × 10^-n. That loop takes several times to have a stabilized consistent result. Depending on the cycle parameters there can be a significant differance between the first state calculated and the stabilized one. Then there is a differance in how the initial residual steam state is calculated. A free expansion from end of expansion to exhaust pressure or isentropic.

How do you calculate the residual state? A free or isentropic expansion from release to exhaust pressure.

Test books state it to be a free expansion. George said it should be isentropic. I have no actual data to prove it one way or another. I tend to go with the text book untill proven different. We really are in need of an instrumented expander to actually test some specifics. The books I have are old. Last printed in 1935. Havn't found newer books that fully cover partial expansion cycles of piston engines.

Using the text book description of the precesses of a partial expansion cycle adding compression and clrarance results in significantly higher efficiency. That efficiency improvement comes from elimination of clrarance losses. There is a significant differance in calculated results depending on the state change from release to exhaust pressure process used in calculating the initial residual steam state. Depending on the pressure differance. There is no question of the initial state for full expansion.

Looking at the temperature charts in a Stumpf's books the high temperature just before admission would seam to indicate a free expansion at release is correct or a significant over compression is occurring. The insignificant temperature increase at cutoff tends to indicate over compression.

I think a test expander having sensors built into it could give some valuable information. Pressure sensors at various places. Steam chest and cylinder head. Need thoes expansive high speed and high temperature type. Temperature sensors arrayed in the cylinder wall, in the cylinder head, steam chest and exhaust flow.

Personally I think a counter flow engine having separate admission and exhaust valves would is the best design for automotive use. Such an engine can run with compression to inlet pressure or with little or no compression depending on the situation. At very low speed you won't long overlapping admission and little or no compression. At higher speeds where efficiency is important you won't high expansion and compression to eliminate clearance loss.

All this theory is looking at a single steady state conditions. There are infinitely many states in a power range. There is no single cycle that meets all requirements. Efficiency is much less important tooling around a parking lot then on the highway.

We are not really interested in efficiency as much as fuel consumption. That is we are interested in the MPG figures. It takes more power to run at higher speeds. So for best all around MPG we need to target normal highway speed efficiency or general open road efficiency.

We know that the full expansion cycle in theory is the most efficient. We are able to get most of the compression work back on expansion. So compression is a possible power control method with little efficiency loss. My idea of varying clearance is one method. Another that might work is to return steam to the steam chest. That is a counter flow engine that once compression pressure reaches the steam chest pressure it is basically compressed into the steam chest were it's compression-pump work is returned on the power stroke. That allows power to be controlled by exhaust valve closure. Such a scheme could be a full expansion cycle with power control by compression work that can be recycled. That is the basic idea behind my variable clearance engine. At least the efficiency loss is not going out the exhaust port as with a partial expansion. It still is a bit more complicated control as a different mode is required at low speed.

The higher the pressure the higher the expansion ratio we can run. But on the other hand we need variable power. Finding the best solution is finding the best methods of power control for all operatoring conditions. And within the design constraints of meterials used.

We basically need to control engine torque. Torque can be controlled by throttling, cutoff, and compression. The most efficient control soloution would combine them.

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