Isothermal Heat Transfer

[Fool]

Isothermal Heat Transfer

In a Stirling Engine there are two heat exchangers. Call them the hot plate and cold plate for this thread. There are other configurations but they behave similarly, so it's not meant as a limitation. The hot plate will be at Th and the cold at Tc.

The displacer pushes the internal working gas, to be referred to as the "gas", from the cold plate to the hot plate. Back and forth in a piston like fashion. The volume of the gas changes little because of this action. The displacer blocks and insulates the opposite plate.

The displacer has an integral regenerator that warms the gas as it is pushed toward the hot plate and cools it when pushed toward the cold plate.

An engine running at 600 RPM is experiencing 10 complete cycles per second so a single stroke is about 1/20 second long, or 50 milliseconds.

The regenerator heats the gas up some but not quite to Th. It hits the hot plate with a Delta T, DT, temperature difference. With any DT heat will begin flowing immediately, how much and how fast depends on the temperature difference, gas, and surface area, also the thickness of the gas and flow across the plate.

Even after the entire gas is pumped, by action of the displacer, into the hot zone, flow continues in a forced convection process caused by gas momentum.

The power piston begins expanding the gas. Gas pushing on piston, piston moving a little faster. Still approximately 600 RPM. Expansion causes temperature drop. More DT. Heat rushes in faster. No matter how fast the expansion is, some heat will get in. The bigger the surface area the closer to Th.

Heat getting in during expansion increases the energy to work conversion. This process requires a DT to work. Since the piston and displacer are moving in approximately sinusoidal motions the heat transfer will not be a perfect isotherm. The DT will vary. There will be a DT for the entire stroke.

The faster the engine runs the greater will be the DT. This tends to limit the RPMs. The upshot of this is that the inside isotherm will be lower than the hot plate temperature.

This is not an adiabatic expansion.

An engine unloaded will tend to run faster, and pull in less heat per cycle. A faster running engine isn't necessarily working harder or better.

The reverse is true on the cold plate. DT will be about the same. The energy rejected will be less because and in proportion to the colder temperature. This will save energy during compression, and produce a positive work energy out for the complete cycle. And also isn't Adiabatic.

Not Th or Tc, but definitely not adiabatic. Sort of a Th-DT and Tc+DT isotherm.

[VincentG]

What are you driving at?

[Fool]

I think it goes along with your experiments. Somewhere someone made the claim that Stirling Engine expansion is "more adiabatic". I think that is misleading.

https://en.m.wikipedia.org/w/index.php? ... prov=rarw1

"This article is about the adiabatic Stirling cycle. "

Very misleading.

Without heat going into the gas somewhere during the expansion stroke, power to weight will greatly suffer.

Improving the heat input, especially during expansion seems like a very good thing to strive for.

[VincentG]

I certainly agree that heat needs to be continually added during expansion. The quantity/time heat is added is exactly the means by which I plan on throttling my engine, by varying max displacer lift.

I am under no delusion that a completely isothermal cycle can be achieved at high cycle rates, but to build an engine that is not capable of nearly isothermal performance at static or very low cycle rates seems silly. And that's about all I have seen in my research.

An engine that is nearly capable of isothermal operation as a prime mover, should be nearly capable of isothermal operation as a heat pump. The heat pump will always have the efficiency advantage as the hot and cold plates can and should be colder and hotter than the gas, in that order, and so minimizing thermal bridging.

When I do these unloaded volumetric expansion tests, it's interesting to note that under those conditions the chamber is not a heat pump or a prime mover. You are just observing the behavior of the gas free to expand and subsequently be compressed by the atmosphere. So to what level does either affect the behavior of the gas? In a piston engine(or heat pump), it is not Cv or Cp in operation.

[matt brown]

I think it goes along with your experiments. Somewhere someone made the claim that Stirling Engine expansion is "more adiabatic". I think that is misleading.

https://en.m.wikipedia.org/w/index.php? ... prov=rarw1

"This article is about the adiabatic Stirling cycle. "

Very misleading.

Without heat going into the gas somewhere during the expansion stroke, power to weight will greatly suffer.

Improving the heat input, especially during expansion seems like a very good thing to strive for.

There are so many factors to consider when scheming ECE, but nixing heated working cylinder is near top of list. Recent zero-zero buzz reminded me of similar one-one buzz regarding PVT values that approach one, similar LTD. Here's an Otto scheme that's under the radar

Otto PV Geo.png (98.82 KiB) Viewed 4277 times

Sorry for the extreme values, but Geogebra app doesn't allow scale changes. Basic scheme is low volume ratio Otto where

(1) 2:1 volume ratio is still common Stirling ratio
(2) "zero point" isobar to allow 'buffer' compression
(3) both charge AND buffer pressure are above ambient

Despite this crazy 300-1050k cycle (due to app limits) check out the regen potential where the 2-3 isochor is 800k >>> 300k vs 4-1 isochor 400k >>> 1050k. Indeed, when approaching one-one values, things change, and an Otto cycle may include substantial regen. Here, 80% of normal sink heat can be regen to input (400-800k "sink" to 400-800k "source") which drastically alters 'normal' Otto eff.

Meanwhile, consider similar Stirling cycle

Stirling PV Geo.png (98.23 KiB) Viewed 4277 times

Note similarities and differences between this Stirling and previous Otto, especially same volume and thermal ratios. Ha, this Otto is still 3/4 the output of vaulted Stirling.

[matt brown]

Sorry for the extreme values, but Geogebra app doesn't allow scale changes. Basic scheme is low volume ratio Otto where

(1) 2:1 volume ratio is still common Stirling ratio
(2) "zero point" isobar to allow 'buffer' compression
(3) both charge AND buffer pressure are above ambient

Despite this crazy 300-1050k cycle (due to app limits) check out the regen potential where the 2-3 isochor is 800k >>> 300k vs 4-1 isochor 400k >>> 1050k. Indeed, when approaching one-one values, things change, and an Otto cycle may include substantial regen. Here, 80% of normal sink heat can be regen to input (400-800k "sink" to 400-800k "source") which drastically alters 'normal' Otto eff.

I'm lazy in my old age, so didn't attempt actual calcs on this Otto cycle, but basic Otto is just shy of Carnot = .25 (via my adiabatic PVT cheat sheet) since it reduces to simple function of dT for each adiabatic process. Assuming W = .25 cycle heat then sink heat = .75 cycle heat when this Otto lacks regen. However, when regen is added, we regen 80% of "sink" heat to "source" heat where "80%" of .75 = .60 cycle heat, thus .25 + .60 = .85 eff and super-Carnot, since Carnot = .71 here, like Stirling above. The only magic here is regen scheme that shrinks normal Otto sink heat from .75 cycle heat to mere .15 cycle heat.

Gadz, that wasn't so hard, trumping Carnot and Stirling fanboys in one swoop. OK Fool, your turn...

[Tom Booth]

... Somewhere someone made the claim that Stirling Engine expansion is "more adiabatic". I think that is misleading.

https://en.m.wikipedia.org/w/index.php? ... prov=rarw1

"This article is about the adiabatic Stirling cycle. "

Very misleading.

Without heat going into the gas somewhere during the expansion stroke, power to weight will greatly suffer.

Improving the heat input, especially during expansion seems like a very good thing to strive for.

Hmmm ...

Back in my high school Small Engine Repair course we learned about ignition timing.

Ignition after TDC we learned was not good because the engine is still running on the momentum of the previous cycle.

So, "adding heat" (the equivalent of ignition & combustion) "during expansion" is like trying to push a wagon while the horse is running away with it. The expanding gas has little effect on a piston that is swiftly moving away.

Then what happens is there is little transfer of energy. Without resistance there is no transfer of energy.

In an IC engine the result is very low power.

In a sealed external combustion engine you have, at BDC a cylinder full of heated expanded air that hasn't done any work so hasn't lost energy to bring down the pressure and temperature enough to allow compression.
So, time the "ignition" as near as possible to TDC while the piston is stationary, then the expanding gas meets resistance. The expansion transfers the maximum amount of power to accelerate the piston.

Or, in actuality, because heat transfer takes a bit of time, advance the ignition to some degree BEFORE TDC.

In practice, in a Stirling engine the standard timing is to start introducing heat a full 90° before TDC but, in an IC engine that much advance would cause real problems.

In other words, adding heat while the piston is "running ahead" is a waste of energy. You don't want the expanding gas chasing the piston down the cylinder. You want the heat input to be at TDC when the piston is stationary so the expanding gas can actually PUSH it, accelerating it from a standstill. Then, as it "runs ahead", you may just as well curtail the heat input because you're never going to catch up anyway. Any heat input after the piston is "running ahead" will just get in the way, causing back pressure on the return stroke.

[Tom Booth]

Here is a Google AI summary that I think is somewhat applicable:

A gas expanding into a vacuum, also known as free expansion
, does no work because there is no external force opposing the expansion. Work is defined as the force applied on an object times the displacement of the object in the direction of the force. In a vacuum, there is no external pressure, so the system does not need to use energy to push the gas against any external pressure when the gas expands.

From one cycle to the next, the piston is driven, not just by the heat input from the current cycle but the momentum from the previous. So heating and expanding the gas late, after TDC is nearly equivalent to the situation described here, "free expansion" into a vacuum.

So, most of the heat input should be very near TDC and perhaps 1/3 or so of the way into the power stroke before the piston takes off running down the cylinder and while it is still relatively idle near TDC. After that the piston will be "running ahead" and additional heat input becomes counter productive.

This has been known since Watts experiments with the steam engine. Under a very heavy load that could be extended to some point short of BDC to some advantage but in general you want enough adiabatic expansion to bring the temperature and pressure down before the return stroke, then you don't have an issue with resistance from "back pressure" due to excessive heat input that is impossible for an engine running at high RPM to fully utilize.

Now maybe there is some better way but that is the basic reason why real engines tend towards adiabatic.

So saying REAL Stirling engines are "more adiabatic" is not misleading at all. REAL engines in general are almost always "more adiabatic". It's just a fact.

[Fool]

I don't see it. The gas in a Stirling is always in contact with the hot plate or cold plate. This indicates heat transfer any time the gas is a different temperature. Timing has nothing to do with heat transfer. The gas on the hot side picks up heat until moved to the cold side where it loses heat until moved back to the hot side.

Your ICE comparison is nothing more than a bad analogy. Fuel burns in any ICE from ignition near top dead center, to bottom dead center and after. Valves or ports open and burning fuel enters the exhaust still at top temperature. There's no adiabatic expansion process. Flame shoots out the exhaust.

Steam engines have valve adjusters. They can be set to blow a small puff of steam at TDC to be expanded, or blow steam for the entire stroke if maximum force is needed.

[Tom Booth]

I don't see it. The gas in a Stirling is always in contact with the hot plate or cold plate. This indicates heat transfer any time the gas is a different temperature. Timing has nothing to do with heat transfer. The gas on the hot side picks up heat until moved to the cold side where it loses heat until moved back to the hot side.
.....

So you don't believe in the concept of heat being converted to mechanical motion.

If heat is transfered into the engine, the only way it can leave is to be transfered out "to the cold side".

You don't think the gas can ever be a different temperature due to "work" output.

Is that right?

[Tom Booth]

Anyway, here is someone else's opinion:

too little advance or retarding the ignition will push the piston down as the crank is pulling it down which will reduce the force of the gas expansion.

https://www.pistonheads.com/gassing/top ... &t=1347125

If you think the principle doesn't apply to Stirling engines, your certainly entitled to your opinion.

I can understand why you have flames blowing out your tailpipe.

[Fool]

I'm fairly sure you don't read my posts . From the opening post :

The power piston begins expanding the gas. Gas pushing on piston, piston moving a little faster. Still approximately 600 RPM. Expansion causes temperature drop. More DT. Heat rushes in faster. No matter how fast the expansion is, some heat will get in. The bigger the surface area the closer to Th.

What part of "Expansion causes temperature drop. " is not energy leaving as work. Colloquially, conversion of heat, correctly conversion of internal energy. Correctly heat enters and leaves as heat under the force of temperature difference. Heat becomes or comes from internal energy. Work and heat are two different forms of energy flowing. Technically internal energy as pressure get converted to work. W=P•DeltaV.

Energy can only leave as heat if the walls are cooler than the gas. Enter if hotter. And it does so beginning immediately apon contact with that difference. Adiabatic only works, almost never, if the walls are the same temperature as the gas. The gas never stays the same temperature during adiabatic expansion or compression.

[VincentG]

Tom is proposing that heat energy disappears and the internal energy of the gas reduces after becoming mechanical motion.

Fool is arguing that internal energy remains constant and that the temperature reduction is purely from a reduction in pressure due to expansion.

Is that accurate?

[Tom Booth]

Tom is proposing that heat energy disappears and the internal energy of the gas reduces after becoming mechanical motion.
...
Is that accurate?

Except that I don't consider "heat energy disappears" and "internal energy of the gas reduces" two separate. Operations.

Heat going in becomes "internal energy".

Presumably incorporated in some way into the expanding gas. Gas "expanding" is just another way of saying the gas molecules "increase kinetic energy".

The more energetic molecules impact the piston in some way transferring the energy to the piston which moves down the cylinder.

Basically all just transfers of molecular kinetic energy. From the molecules of the hot plate to the working fluid to the piston, like so many billiard balls.

At the end of the series of operations there is no"heat" that was supplied remaining in the working fluid. The working fluid only acted as an intermediary for transferring energy to the piston.

There is then no need to transfer "heat" to any "sink".

Fool stated: "This indicates heat transfer any time the gas is a different temperature."

He will have to explain.

But IMO a temperature difference can be the result of "work" output. Energy transfered to the piston from the working fluid in a way that I would not describe as a "heat transfer".

Fool, and the Carnot theory generally seems to think or say heat can be converted to work but still needs to be removed in the form of heat afterwords. Like water turns a turbine transferring some energy but the water [or for heat "calorics" (? Fools term?)] still has to pass through and out the other side.

By Kinematic Theory: all the energy, heat or otherwise can't go straight through a Carnot Engine. You are confusing Calorics with heat energy. Calorics are just carriers. They carry different quantities of heat as specified by the temperature. They go in the top at Th and come out the bottom at Tc

[Tom Booth]

Compress_20240423_154122_2561.jpg (21.53 KiB) Viewed 4161 times

Don't ask me.