Engine Pressurization

[stephenz]

yes, the thinner the cross section of the regenerator material is, the less important thermal conductivity is.

Gas flow rate in an given engine are easy to estimate, just based off the volume swept by the piston/displacer. These values get pretty high as RPM go up.

[matt brown]

Matt can you try to explain in layman's terms what you mean by regen heat>input heat? You always lose me here.

sq cycle.jpg (58.59 KiB) Viewed 1704 times

Vincent, take a lot at this PV and notice

(1) regen isochors 2-3 and 4-1
(2) Thigh 3-4 heating
(3) Tlow 1-2 cooling

The downside of any PV is that they kinda distort reality. IOW the regen isochors here represent the same amount of heat (watts, joules, BTUs, whatever) although isochor 4-1 is 'shorter' than isochor 2-3. Per previous posts, there's no trip odometer around PV showing values, but the regen heat (2-3) is greater than the input heat (3-4).

My ranting on 'regen load' is merely to quantify the ratio of regen heat to input heat. The obvious conclusion is simply the inverse where LESS heat is req'd during THIS isothermal expansion 3-4 than regen 2-3. If mech allowed a greater volume ratio than shown here, and more input heat was provided at 3-4, then more work would be provided (from more input) but while THE REGEN HEAT REMAINS THE SAME. In this manner, the regen load would be decreased. Conversely, if you raise Thigh 3-4 while keeping this original volume ratio, then regen load would be increased.

Effective regen functions as both an internal heater & cooler, and inefficient regen requires more external heating & cooling (and usually larger heater and cooler). Due to mech constraints hovering around 2:1 volume ratio, comm'l SE have high regen load due to high thermal ratio. So, the average comm'l SE is pitting the loss from regen inefficiency compounded by regen load against the Carnot gain from a higher thermal ratio.

Feel free to beat me on the head if still lost.

[matt brown]

I'm glad I'm not the only one questioning why literature says the best regenerator would have low thermal conductivity and high specific heat.

I kind of get why high specific heat and high density would be useful, but I only see this useful as a mostly practical parameter: making the regenerator smaller. There is a finite amount of heat that the renegerator needs to retain, any more than that and it's wasted mass/volume/etc.

But thermal conductivity, I don't see how high thermal conductivity would be a bad thing. Perhaps, they mean as to not "conduct" the heat away to a housing, and ultimately through the environment? not sure, I looked and never found compelling data showing why thermal conductivity was bad.

That's one of the things I am going to try. I have samples of very similar density and heat capacity of materials with widely different thermal conductivity, so hopefully the testing will be conclusive enough to learn something.

I am trying to get all samples into a pressure drop test. Air compressor -> test rig -> flow meter. Test rig is a housing with a cylindrical sample of known diameter and length, in which compressed air is going through. it has a pressure sensor before and after to measure the pressure drop across the sample. By logging the data in real time and varying the input pressure, I'll be able to gather precious Pressure Drop Vs Flow Rate data

There's been so much regen talk over the decades that regen is a mess. There's simply so many different issues that a correct reply for one thing is incorrect for another. Example...I think that a low thermal conductivity mainly refers to a bulk matrix like steel wool which is more vulnerable to thermal short then isolated baffle plates.

Years ago, I was considering the same regen tests until I went down a rabbit hole concerning porosity vs surface area vs dP where everything appeared as competing issues. I later concluded that regen volume was not a massive issue when design incorporates this volume. I think the trick here is carefully gaming pressure after compression vs pressure after expansion.

[matt brown]

One night while, as Matt would say, in an altered head state, I was thinking of SE efficiency and I pictured a cartoonish animation of an ideal heat engine. You may picture it as a snake that ingests a volume of hot air. The warm bubble of air turns the small traveling expanded section of snake red as it passes through, while the moment it moves through, the previously red hot section instantly cools down and progressively the heat is dissipated into the work output of expanding the snake.

Love this, bitten by the bug, I recognize the symptoms. I've had several such visions falling asleep while staring at screens or drawings. Only seems to work for me with SE issues when my 'alpha' state is emerging - lol

All kidding aside, any solution will probably come from some type of altered state where the dots are not connected in a straight line. So many guys have approached this in a linear fashion to no avail.

[Tom Booth]

I think one thing, as far as I know, always overlooked, except in some text on Stirling heat pumps and the like, is that the regenerator stores and returns to the hot side heat of compression, perhaps more than primary input heat

In an Alpha, at one point in the cycle, the air is compressed into the regenerator by both pistons. This generates a high temperature throughout the working fluid which the regenerator absorbs. After that the hot side piston draws air through the regenerator into the heated cylinder.

With expansion, the working fluid is cooled. Now the already cold regenerator, cold due to the heat having been drawn out to the hot side, is cooled further, due to cooling by expansion.

The hot side piston then pushes this cold air through over to the cold side.

The various online animations of Alpha engines in operation don't do justice to this heat pump aspect of a Stirling engine regenerator.

To illustrate, imagine a fire piston with steel wool in the bottom. Compress the air and the steel wool will absorb the heat. Now imagine a piston at the bottom that pulls away drawing the heat off from the steel wool. Now pull the plunger back up. The air will now be colder above the steel wool.

[Tom Booth]

I think it is actually mostly incorrect to think of a Stirling engine as having isolated pockets of hot and cold air. The entire volume of air is compressed/heated then expanded/cooled.

[stephenz]

Effective regen functions as both an internal heater & cooler, and inefficient regen requires more external heating & cooling (and usually larger heater and cooler). Due to mech constraints hovering around 2:1 volume ratio, comm'l SE have high regen load due to high thermal ratio. So, the average comm'l SE is pitting the loss from regen inefficiency compounded by regen load against the Carnot gain from a higher thermal ratio.

isothermal.gif

The image above is for an ideal cycle, and of course the temperature is not going to be constant in the heater, and isn't constant in the cooler either.
I've never seen a paper of a SE equipped with sensors showing the temperature compression space, cooler, heater, expansion space; let alone regenerator. But one thing that I think this diagram shows well is the linear temperature gradient that a proper generator should achieve. Ideally the average temperature inside the regenerator should be constant over time, and the gas going through it should ramp up or down pretty linearly.

Practically, the regenerator acts as a pulse cross flow fluid/fluid heat exchanger. The gas is heated/cooled by its "past self" a few tens of millisecond earlier.

As such, if it wasn't for added volume and added pressure drop, oversizing the regenerator wouldn't that bad. Looking at the shuttling of the gaz from hot expansion space to the cool compression space, dumping all that heat straight into the cooler will increase the cold temperature negatively affecting efficiency directly by reducing the work done. Same thing applies to the shuttling in the other direction.

My version of that diagram would be more like this:

cycle temperatures.png

Where the gas temperature gradient inside the regenerator would go up and down due to fact that we don't have isothermal compression/expansion. I.E. compression will raise the gas temperature some and expansion will decrease it. This gradient is the result of imperfect cooler and heater.

pardon the crude paint work

[Tom Booth]

Taking some liberties with the diagram posted by Matt

Polish_20230515_013250573.jpg (503.09 KiB) Viewed 1673 times

1 to 3 is the "fire piston" down, compression, heating stroke.

3 and 4 is the second piston drawing out the "heat of compression" from the regenerator.

But there are a few things missing. Like there should really be a 5, where the power stroke results in a general cooling of the working fluid where Both pistons are extended/expanded away from the regenerator.

Also, some color could be added to the regenerator to show temperature changes within the regenerator.

Heat can only enter the working fluid from an external source after a general cooling of the working fluid after expansion/power stroke (at 5 which is not shown)

[matt brown]

isothermal.gif

As such, if it wasn't for added volume and added pressure drop, oversizing the regenerator wouldn't that bad. Looking at the shuttling of the gaz from hot expansion space to the cool compression space, dumping all that heat straight into the cooler will increase the cold temperature negatively affecting efficiency directly by reducing the work done. Same thing applies to the shuttling in the other direction.

I prefer to consider cycles first as distinct idealized events then reconsider whatever reality has issues. An inline heater & cooler has pros & cons, but note that under ideal conditions, the low pressure blow after expansion does NOT sink to cooler, it's only the compression process that (ideally) sinks to cooler.

If 4 distinct events per cycle (vs typical out-of-phase cycle) I doubt regen volume matters. I think the most important regen issue is matching the regen heat 'capacity' to the gas heat capacity (volume x dT). I suspect that this is a major issue you will be testing, not just flow, dP, porosity, etc.

Furthermore, when 4 distinct events (aka clean cycle) the alternating HP & LP regen blows are very similar with only a small rise & fall of temperature gradient across regenerator.

[matt brown]

I think it is actually mostly incorrect to think of a Stirling engine as having isolated pockets of hot and cold air. The entire volume of air is compressed/heated then expanded/cooled.

I agree 100% and blame the academics who simplify stuff to increase accessibility at the expense of accuracy.

[matt brown]

In an Alpha, at one point in the cycle, the air is compressed into the regenerator by both pistons. This generates a high temperature throughout the working fluid which the regenerator absorbs. After that the hot side piston draws air through the regenerator into the heated cylinder.

Although I hate the typical out-of-phase aspect of common SE, you raise a rare point: consider typical SE with 90 deg phasing where both pistons are compressing, and assuming all work can become heat, all this ('excess') Wneg might rob output, but the increased heat will reduce source input. I've never seen anyone mention this until now, and suspect this justifies the adiabatic analysis which crept into SE buzz decades ago, but slowly. The downside here is that this screws up regen (constant temp gradient) and moves a Stirling cycle towards an Otto cycle with less efficiency. Meanwhile, the upside here is a valid cycle remains and makes the best of a bad thing (lame phasing).

[matt brown]

To illustrate, imagine a fire piston with steel wool in the bottom. Compress the air and the steel wool will absorb the heat. Now imagine a piston at the bottom that pulls away drawing the heat off from the steel wool. Now pull the plunger back up. The air will now be colder above the steel wool.

This reminds of a scheme where a guy added a third piston/cylinder to SE regen to add & remove heat & pressure. Surely, outside the box, but not as wacky as it seems initially. There's so many ways to skin this cat...

[VincentG]

I'll post a video to later to support what I'm saying here. I tend to think that the compression and expansion of the working gas by the power piston is not a primary part of the stirling cycle but merely a consequence of extracting usable power.

If I run my ltd engine by hand with the pressure guage connected but the power cylinder plugged with a stopper(ie no power piston), there is still heating and cooling, expansion and compression albeit at the ideal constant volume that seems to elude us all.

If we could grab onto that molecular energy with some sort of oscillating turbine(or resonance, or something) we get our energy out without any additional expansion and contraction.

Point is, maybe the function of the regenerator should be analyzed with just a displacer cylinder in order to reduce variables.

[stephenz]

I prefer to consider cycles first as distinct idealized events then reconsider whatever reality has issues. An inline heater & cooler has pros & cons, but note that under ideal conditions, the low pressure blow after expansion does NOT sink to cooler, it's only the compression process that (ideally) sinks to cooler.

Why not? on an ideal cycle, you're right because the ideal cycle assumes the temperature coming out of the regenerator is the same as the cooler temperature, so there can't be heat exchange here. However, in reality gas will come out of the regenerator with a temperature greater than that of the cooler. Resulting, in the gas getting cooled further as it enters the cooler space before the compression starts.

At least that's what I was trying to capture.


In line heaters/coolers are pretty much the only option for Alpha's considering the physical distance between the 2 pistons. In Beta's (and Gamma's) the cylinder itself act as heater/cooler though they don't make for great heat exchangers.

Ultimately the system's performance and efficiency is bound by how low the gas temperature gets to while coming out of the cooler during compression.

[Tom Booth]

I prefer to consider cycles first as distinct idealized events then reconsider whatever reality has issues. An inline heater & cooler has pros & cons, but note that under ideal conditions, the low pressure blow after expansion does NOT sink to cooler, it's only the compression process that (ideally) sinks to cooler.

Why not? on an ideal cycle, you're right because the ideal cycle assumes the temperature coming out of the regenerator is the same as the cooler temperature, so there can't be heat exchange here. However, in reality gas will come out of the regenerator with a temperature greater than that of the cooler. Resulting, in the gas getting cooled further as it enters the cooler space before the compression starts.

At least that's what I was trying to capture.


In line heaters/coolers are pretty much the only option for Alpha's considering the physical distance between the 2 pistons. In Beta's (and Gamma's) the cylinder itself act as heater/cooler though they don't make for great heat exchangers.

Ultimately the system's performance and efficiency is bound by how low the gas temperature gets to while coming out of the cooler during compression.

There is a chart someone posted in here, taken from a Wikipedia posting that purports to be actual reading from a "real" engine by some accounts or a computer simulation by another account, presumably considered accurate, or based on actual measurements as far as possible.

Taking live rapidly fluctuating temperature readings directly is problematic due to thermal lag within the measuring device, but can likely be determined indirectly.

Honestly I don't know how the graph was produced, but it shows the temperature of the working fluid as being colder than the "heat exchanger" due to cooling by expansion.

In other words, as I related earlier, at the extremity of the power stroke, the gas is expanded, it has also lost energy as a consequence of the power or "work" output.

https://en.m.wikipedia.org/wiki/Stirling_cycle

See the section: "Temperature vs. Crank Angle"

Temperature_vs_angle (1).png (5.1 KiB) Viewed 1626 times

Unfortunately, what type Stirling engine was "measured" is not made clear, and what "heat exchangers" are being referred to is not specified. The hot and cold (heat input and sink) or regenerator.

At any rate the statement there is:

"The gas temperature fluctuations are caused by the effects of compression and expansion in the engine, ..."
And "...the gas temperature deviates above and below the heat exchanger temperature..."

Between about 240° around to 50° (expansion phase) the gas temperature is indicated to be below the heat exchanger temperature.