Author Topic: Talking Thermodynamics  (Read 93532 times)

Online MJM460

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Re: Talking Thermodynamics
« Reply #30 on: May 14, 2017, 12:20:11 PM »
Ideal Gas Laws

Great to see the continuing interests in this topic.  Thank you to all those who have contributed, as well as those who are just following along.

I will address some of the comments later, but first, thank you Paul for highlighting the point that there may be qualifications I should have included in my summary.  So no, better not too quote the initial result without qualification.  The result is really only valid for the conditions assumed for the calculation.  First it is for the expansion part of the stroke only, when both inlet and exhaust valves are closed.  I assumed a start pressure for each calculation of approximately 15 psi as suggested in an earlier thread.  I have worked in metric units so I have made small adjustments and used the values for the nearest value listed in my steam tables to minimise interpolation.  I have also assumed an adiabatic process, with everything up or down to  a steady temperature and no heat gain or loss to the atmosphere.

For air I assumed 17 deg C, on reflection 27 might have been a better choice.  Again to use table entries directly.  Obviously, steam at 17 deg C would be fully condensed, so I used 150 deg C.  This temperature would be reasonable if steam was generated in a boiler at 50 psi, and throttled to 15 psi then some heat loss in the delivery pipe.  Not identical conditions, but attempting to be realistic.  After expansion (2:1), steam tables indicate the steam will be condensing at about 95 deg C.

It is this proximity to condensing that is the reason for a large part of the departure from ideal gas laws, and when condensing starts the ideal gas law does not apply at all.  The heat released in condensing causes the pressure to be much higher than predicted by the ideal gas laws, and consequently, the extra work.  I must admit to never having thought of it in this detail before.  Thank you Jo for pointing me in this direction.  I look forward to learning what other surprises you have in store for us.  I have learned heaps.

You might ask what if I had assumed hotter steam so that it did not condense.  I believe as you get further away from the condensing area, the behaviour gets closer to the ideal gas law, but I expect the departure would be quite significant until the temperature gets quite high, dangerous and rather impractical for our purpose.  I have not done further calculations as they are rather tedious without a specialised computer program, even with a calculator.  I am trying to keep to the issues that potentially have practical application in our model building, and have not spent time in purely theoretical explorations.

The big deal about ideal gas laws?  I probably did not make this clear enough.  When we try to calculate the work done by an expanding fluid, the only things we really know are the starting pressure, temperature, and density of the fluid, and we carry the calculation to the end point at which we know only the volume and fluid composition.  Note we do not know what the pressure and temperature will be.  Early work on this problem (Boyle and Charles are two names that come to mind) gave rise to the ideal gas law which was found to be closely approximated by many gases.  Without this gas law, we do not know how the pressure varies throughout the expansion and cannot calculate the work done.. 

When the ideal gas law does not apply, we basically have to rely on empirical data, such as that contained in steam tables which contain the results of huge amounts of experimental work.  For air there are tables of standard integrals which account for the much smaller but real departure from ideal gas.  Both steam tables and standard integrals for air were used in my calculation, however we should keep in mind that the number only applies for the assumed start conditions. 

Let me try if this summary stands up: While the inlet valve is open enough that the pressure is essentially constant, there is no significant difference in air or steam or carbon dioxide or other gases, however, if our valve gear has both inlet and exhaust valves closed so the work is done by gas expansion, then steam will indeed produce more work than air at the same pressure.  We can finally agree with the old timers on that one.

Kerrin, I had a short assignment at Kapuni some years ago.  Beautiful country in the shadow of Mt Teranaki.  And black sand on the beaches.  Please keep the references to useful sources coming in.  We will talk about condensers and other equipment a bit later, but next time I plan to try and make progress where we started, on the cylinder.

MJM460
The more I learn, the more I find that I still have to learn!

Offline Dan Rowe

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Re: Talking Thermodynamics
« Reply #31 on: May 14, 2017, 02:36:17 PM »
James Watt invented the steam engine and most writers believe he also invented the steam engine indicator. The second invention is not as widely known because he kept that one secret to keep ahead of the competition.

With a steam engine indicator, we have a PV curve for the full stroke of any piston engine. I have taken indicator cards on a 900mm bore slow speed diesel engine.

The reason I linked this thread to the Porter air locomotives is that it has PV diagrams for air engines. There are lots of sources of PV diagrams for steam engines but they are a lot harder to find for air engines.

I for one wish I could look at one of the historic diagrams and be able to say that was good or that was bad, but my study of the diagrams has not progressed beyond getting Peabody's book on the subject. (Cecil Peabody was the head of Marine Engineering at MIT)

Here is an article on the invention of the steam engine indicator and it has a list of sources on the last page.
http://www.farmcollector.com/steam-traction/story-steam-engine-indicator?pageid=1#PageContent1

Dan
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Offline Dan Rowe

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Re: Talking Thermodynamics
« Reply #32 on: May 14, 2017, 06:41:10 PM »
Here is Figure 4: Idealized indicator diagram, from the article linked in the last post.
Illustration by Bruce E. Babcock



Dan
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Offline derekwarner_decoy

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Re: Talking Thermodynamics
« Reply #33 on: May 15, 2017, 03:12:31 AM »
I agree understanding what is happening with/within our model steam plants is essential

To achieve this an inexpensive digital laser pyrometer + a small digital [load cell] weight scale and a laser tachometer ...all for approx. $60.00 is inexpensive...otherwise all we can say is my fingers are burnt :cussing:.....& a few pressure gauges installed within the plant + your wrist watch

The specification for my gas tank is 105gm capacity
The net weight is 398gm
With the gas canister @ 26 degrees C, I can achieve a gross weight of 501gm......or 103gm of gas transferred  :ThumbsUp:

The gas discharge pressure from the tank during this example test was 40 PSI, however the gas tank temperature after the fill was ~~13 degrees C
The known volume of water 600ml after 6 minutes boiled and achieved 135 degrees C at the boiler discharge isolation valve [outer casing shell]
This same 135 degrees C indicates as 45 PSI [~~3 Bar] which is the boiler relief valve set point
[from tables, the same 45 PSI actually requires 143.7xx degrees C]

So from here, engine running times/speeds, exhaust steam temperatures from the engine.....to the de-oiler, and the resultant volume/weight of exhaust water can be measured

I am sure many of our members completed Applied Heat I, II & III in theoretical and steam practical work tests during our training in earlier days  :old: , and remembering the principals are important, however from an aspect of these engineering marvels...it is the understanding what is happening within our model steam plant is the real question

Derek

PS 1......Mixed units of Measurement .....a point of explanation is whilst my original training was under the Imperial system, my later and chosen system is SI......however to this day in Australia, the majority of model steam gauges [Miniature Steam Gauges UK] are marketed in Imperial PSI

When monitoring gas pressure, the indication of 40 PSI as a whole number in a visual report, stating that this pressure as an assumed 2.72 Bar from a gauge that has an accuracy of +/- 5% on FSD and reported as such is not appropriate   :disagree:

PS 2......steam table reference added 16/5
 
« Last Edit: May 16, 2017, 11:09:41 AM by derekwarner_decoy »
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Online MJM460

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Re: Talking Thermodynamics
« Reply #34 on: May 15, 2017, 09:46:48 AM »
Indicator Diagrams

Thanks to Dan and Derek for interesting and informative posts.  I will follow up on testing along the lines of Derek's post when we look at the whole plant.  In the meantime, please collect lots of data in preparation.

Dan's post of an indicator diagram is right on cue and right on topic, so I will use that to round out this initial discussion.  For those unfamiliar with this diagram I will try and talk you through it as an indicator diagram provides a pictorial representation of what actually happens in the engine as opposed to prediction by theory, that necessary empirical data.

So we are all on the same page I will assume we are talking about the top face of the piston in a vertical engine, cylinder above the crankshaft.  The indicator diagram is a graphical representation of the variation of pressure within the engine throughout the cycle.  Like Dan, I am not able to tell whether a real diagram is good or bad, but I will try and talk us through what it tells us. 

The horizontal scale is the volume of the cylinder.  The right hand side is bottom dead centre, and the left side is top dead centre.  The part of the scale to the left of the diagram to the zero on the volume scale is the clearance volume when the piston is at top dead centre. 

The vertical axis is the pressure measurement.  The cycle progresses in the direction of the arrows on the loop on the inside of the actual diagram, clockwise.  When the inlet valve opens, the pressure rapidly rises to the steam supply pressure.  The top boundary of the diagram is the power stroke.  The pressure is roughly constant while the piston moves down with the inlet valve still open.  For this part of the cycle, work done by the gas is simply pressure times volume change, regardless of the gas used.

Note where the inlet valve closes.  After this is the expansion period.  With the inlet valve closed, our inlet pressure gauge no longer tells us anything useful about the pressure in the cylinder.  The curve then shows how the pressure might fall as the expansion proceeds.  Again the work done by the gas is the pressure times volume change, but as the pressure is changing, we have to break up the volume change into bits so small that we can consider the pressure constant during each small volume change.  We then add up all work done by the gas during each bit of volume change for the total.  This process is called integration.  Simple when it is said quickly, but we don't actually know the pressure at any point on the curve once the inlet valve is closed, so we can't do the sums.  The shape of the curve as mentioned in earlier posts, depends on the gas composition.  The indicator diagram actually measures the pressure, so solves the problem.

The indicator diagram is produced by an instrument that gets the piston position from the cross head, and has a pressure tapping into the cylinder, and prints out the graph.  This diagram was described as idealised, meaning the instrument was imaginary, and the diagram is to show the concepts.  In Dan's case, the instrument was real and actually measured the pressure throughout the stroke.  The instrument is delicate, expensive and not many of us have access to one.  For various practical reasons, they are only available for slow speed machines.  I know of ones that were made for 400 rpm machines but I do not know the current state of the technology.

The diagram shown is typical of the pressure path for an ideal gas, and the shape is also similar for steam, as enough indicator diagrams have been made on real machines for us to know the general shape.  If we had a diagram for air drawn on top of the steam diagram, we would find that the diagram for steam shows higher pressure than the air diagram throughout the stroke, so that the area under the steam curve is greater than the area under the air curve, meaning more work done by the gas.

What can we learn from the diagram?  First, we can see the work done during expansion is always less than if the inlet valve remained open.  Second, we use less steam and fuel if we have some expansion.  Third, while steam does more work during expansion than air, how big a proportion of the total work for the stroke depends on just where the valve closes, later closing, less proportional difference.  Finally, we need to look at the exhaust stroke before we can understand the lower boundary of the curve.

Looking at the curves, while the calculated end pressure for steam was about 15% higher than the end pressure for air, it is hard to conceive a reasonable pressure curve for steam that would support a large difference in work done, but no doubt that steam would produce more work than air during expansion.  It is likely that the adiabatic process assumption, no heat gain or loss, is responsible for reducing the difference. There is little doubt that the steam engine looses heat to the atmosphere.  This reduces the pressure and hence the work done by steam.  So yes, steam produces more work than air, but the size of the difference is not yet determined.

MJM460
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Offline Flyboy Jim

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Re: Talking Thermodynamics
« Reply #35 on: May 15, 2017, 02:59:43 PM »
Good explanation.

Looking at the diagram begs the question: If the inlet stayed open longer, keeping the pressure in the cylinder higher for longer, wouldn't there be more work (power) produced during the stroke. I'm sure it has something to do with reaching a "point of diminishing returns", but not sure where that would be.

Jim
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Offline Dan Rowe

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Re: Talking Thermodynamics
« Reply #36 on: May 15, 2017, 04:12:51 PM »
Jim,
The term used for the point in the stroke that the valve gear closes the inlet valve in a steam engine is known as cut off.

This is expressed as a percent of piston stroke, so 100% cut off means that the valve stays open the full length of the stroke and is the max power for a given cylinder.

Looking at the diagram in post 32 by eye the cut off point is less that 50% of the stroke it is about 30% of the stroke which gives good economy.

Steam locomotives have a cut off of around 85% for full gear. The dotted line in figure 4 shows the effect of hooking up or notching back the valve gear. The cut off is chosen by the designer for the type of work the steam engine will be doing.

Further reading:
https://en.wikipedia.org/wiki/Cutoff_(steam_engine)

Dan
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Offline PStechPaul

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Re: Talking Thermodynamics
« Reply #37 on: May 15, 2017, 08:48:14 PM »
This is an interesting discussion, and I'm following to some small extent. I wonder how much effect there is based on the sinusoidal motion of the piston due it being connected to a flywheel, and the amount of torque applied based on angular position. There would seem to be some considerable "torque ripple" due to the changing pressure on the piston and its contribution to rotary torque of the flywheel through the length of the stroke. Also perhaps some sort of proportional inlet valve could adjust the volume of steam entering the cylinder to correspond to the position of the piston, and the volume of the chamber.

Offline Flyboy Jim

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Re: Talking Thermodynamics
« Reply #38 on: May 16, 2017, 03:08:05 AM »
Jim,
The term used for the point in the stroke that the valve gear closes the inlet valve in a steam engine is known as cut off.

This is expressed as a percent of piston stroke, so 100% cut off means that the valve stays open the full length of the stroke and is the max power for a given cylinder.

Looking at the diagram in post 32 by eye the cut off point is less that 50% of the stroke it is about 30% of the stroke which gives good economy.

Steam locomotives have a cut off of around 85% for full gear. The dotted line in figure 4 shows the effect of hooking up or notching back the valve gear. The cut off is chosen by the designer for the type of work the steam engine will be doing.

Further reading:
https://en.wikipedia.org/wiki/Cutoff_(steam_engine)

Dan

Thanks Dan. I've heard the term "cutoff" before but didn't know exactly what it was. That helped a couple more pieces fall into place.

Jim
« Last Edit: May 16, 2017, 03:26:09 PM by Flyboy Jim »
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Online MJM460

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Re: Talking Thermodynamics
« Reply #39 on: May 16, 2017, 12:46:07 PM »
The Exhaust Stroke

Thank you for more great contributions, and to everyone else who is sticking with it.  Jim, there are not really diminishing returns, keeping the valve open to the end of the stroke results in the maximum work for a given size of cylinder.  This is not the same as maximum work from a given quantity of steam.  Cutting off early saves steam, so reduces fuel costs, when you don't need the maximum output.  Think of a locomotive going over a hill.  Going up, maximum effort is required.  Then, much less is required when going down the other side, so fuel can be saved by cutting off early.

Glad to have you with us, Paul.  There is a very large torque fluctuation through out each revolution, it even goes negative for a single cylinder engine.  We will be exploring that in the near future.

Thanks Dan for your help in explaining the indicator diagram, it helps me keep these posts a little shorter.

To continue our look at the cylinder, we now need to look at the exhaust stroke.  When the exhaust valve opens, the release point on the diagram, there is no more expansion, and the pressure in the cylinder goes into pushing steam into the exhaust system, where the remaining energy is essentially lost.  At least as far as this cylinder is concerned.

At the bottom dead centre (still thinking in terms of a vertical engine) another very significant change occurs, the piston starts to move upwards.  Why is this so important?  It is because in calculating work done, the two quantities, force and displacement, are vectors.  This means that these quantities have both magnitude and direction.  The cylinder constrains the piston to move only up and down, but opposite directions have opposite sign.  We unconsciously defined down as positive when we multiplied pressure times area to give force then by the piston displacement to give work done by the gas which we assumed was positive.  On the return stroke, the force on the piston is still down, but the piston is moving upwards which must then be negative.  So the work done by the gas in the exhaust stroke is negative.  Alternatively, we can consider that the piston is now doing work on the gas, in pushing the steam out of the cylinder.  This is shown on the diagram as the lower boundary of the diagram until the exhaust valve closes.  Continuing movement (with the inlet valve still closed) results in compression of the remaining gas shown by the upward curve on the left hand boundary of the diagram.  In a well timed engine, the compression achieves close to steam inlet pressure just as the inlet valve opens and the cycle repeats.

So we now see that the work done by the gas during the complete cycle is the work done during the down stroke minus the work done by the piston during the upwards or exhaust stroke.

I might appear to have laboured this point a little, but is really is where "the rubber hits the road" so to speak, in the amazing process of converting the heat from the fuel, to energy in the form of vibration of gas molecules and then to mechanical work.

Next we will look at the piston.  Thanks for following along.

MJM460
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Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #40 on: May 16, 2017, 02:29:03 PM »
Using the planimeter to calculate horsepower and stuff.......

Offline Dan Rowe

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Re: Talking Thermodynamics
« Reply #41 on: May 16, 2017, 07:46:19 PM »
I have only used a planimeter a few times in an engineering lab years ago. It is used to trace the indicator card lines in a complete loop. Knowing the spring constant on the steam engine indicator and the stroke reduction the work done can be calculated. This is known as indicated horsepower.

Peabody spends a bit of time describing the types of error that is involved with using an indicator. These include inertia of the moving parts and friction in the stroke reduction gear and a few other types of errors.

The modern way to do this is with a pressure transducer which will eliminate most of the types of error associated with a steam engine indicator.

The expansion curve for steam is very similar to a rectangular hyperbola. This is sometimes drawn between the point of cutoff and the release point as a standard reference line. It is also used in design to approximate the PV (pressure volume) curve and draw a design best case indicator card which can be used with a planimeter to calculate the indicated horsepower.

http://mathworld.wolfram.com/RectangularHyperbola.html

Dan
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Online MJM460

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Re: Talking Thermodynamics
« Reply #42 on: May 17, 2017, 12:26:35 PM »
The other side of the piston.

Planimeters, those were the days.  I cannot help but marvel at the ability and skills of our fore fathers in designing and making those things.  I got to use one in my Dynamics of Machines subject, but not since.  And attended the 50 year anniversary last year.

So far I have tried to be very consistent in referring to the "work done by the gas" on the piston, specifically on the top face of a vertical engine.

If we consider the sides of the piston, the gas forces are always balanced by the equal and opposite force diametrically opposite.  There can be mechanical forces on the piston sides but these do not concern us at the moment.  However we cannot ignore what happens on the lower side.

There are two arrangements to consider, the first being a double acting cylinder as on the first steam locomotives we ever saw.  Most real working engines are also double acting for reasons that will become obvious if it is not self evident.  The lower side of the piston is in an enclosed cylinder, much as the upper side.  The main obvious difference from the upper side is the piston rod and the provision for it to exit the cylinder through the gland.  The lower face of the piston experiences gas forces, apart from the centre section which is occupied by the piston rod.  The piston rod does not escape gas forces, it experiences atmospheric pressure on its lower end.

The gas force on the lower face is directed upwards, and follows the same cycle as the the force on the upper face, but out of phase, so the lower face is in the exhaust phase while the upper face is experiencing the inlet phase.  Clearly there are two working strokes in each elevation.

When the pressure in the top of the cylinder is highest, the net force is down and the piston moves down, and vice versa.  The net work on the piston is available at the piston rod to overcome friction within the engine and to do the useful external work of the engine.

The situation in a single acting engine is slightly different.  The bottom of the cylinder is open to atmospheric pressure.  When gas is admitted to the top of the cylinder, the piston moves down for the power stroke.  Work is done by the piston on the air in the cylinder to expel it from the cylinder. 

As single acting engines normally exhaust to atmospheric pressure, the cylinder pressure during the exhaust must of necessity be greater than atmospheric pressure.  The force exerted by atmospheric pressure is less than the force from the gas above. Hence the net force on the piston is down, motion is upwards, so work by the gas above the piston is negative.  That is, the piston is doing work on the gas.

There is only one power stroke per revolution for a single acting engine.  During the exhaust stroke, the net output (and torque) is negative, and the engine slows down.  A flywheel stores energy by speeding up during the power stroke, and returns this energy as it slows down on the exhaust stroke.

I might appear to have laboured the point a bit, but without this understanding of how gas pressure converts energy to work, it can be quite difficult to understand why a Stirling engine, which appears to be single acting, under some circumstances is actually double acting.  (A topic for much later!)

Next time, how is all this relevant?

Thanks for following along.

MJM460
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Offline derekwarner_decoy

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Re: Talking Thermodynamics
« Reply #43 on: May 17, 2017, 10:46:40 PM »
Well MJM460...as of this morning we see.... "Topic: Talking Thermodynamics  (Read 1143 times)"

This is always a good indicator [no pun intended] in understanding how many members are reading this thread so from the numbers I suggest you have a good repeat audience  :happyreader: ...yes viewing and reading the work

Derek
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Online MJM460

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Re: Talking Thermodynamics
« Reply #44 on: May 18, 2017, 02:01:22 PM »
Yesterday was just one of those days!

Thanks Derek, yes, it is great to see so much interest.  I have always thought we were a bit too reluctant to get really technical, let alone the maths.  Our aero modeller colleagues include quite a bit of aerodynamics in their literature, so I don't know why we have to apologise before including a bit of thermodynamics.  It is my intention to show how relevant it all is to our engine making.

But yesterday?  It was not a good day.  If you found yesterday's post a bit hard to follow, please don't despair, it did not do much for me either when I read again today.

Just as in building we sometimes don't get a part up to our standard and have to consign it to the scrap bin, in trying to build a knowledge base, the same thing happens.  I assume that is what the "modify" button is for?  I will try it in the next few days and let everyone know when it is ready to read again.  I have at least given thought to how I should have approached it.

But that is not the complete reason for my heading.  Earlier in the day, I was working on the brown stuff, when my jigsaw went bang, and all the lights went out.  The machine was not even warm, and I did not see any smoke get out.  So I reset the breakers, restored the lights and tried to start and again bang and no lights.  It was only about 25 years old, but clearly a trip to the tool shop was required.  The man did not miss a beat.  What a pity you did not bring it in last Friday, he said.  It might have still been on warranty!  I was not quick enough to point out it was not broken then.  It was really disappointing.  Despite using power tools since primary school, that is the first I have ever broken.  But the new one is really nice. 

To top it all off I found that my belt sander was so old that the correct size belts do not seem to be available.  (Much older than the jigsaw, it was my Dad's.)  Looks like more tool shopping required.  What a blow!  I never saw what others see I retail therapy, then one day I happened on a really good tool store.  Now I get it.

I have resolved some internet technologies this week, so I will prepare a diagram to illustrate where we are up to, as I should now be able to communicate with the scanner.  But it has been a long day, and it is late, I will be very lucky to to get any thinking time tomorrow so it may be Saturday.

Thank you for all the interest.

MJM460
The more I learn, the more I find that I still have to learn!