Author Topic: Talking Thermodynamics  (Read 194397 times)

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #630 on: January 02, 2018, 12:36:54 AM »
<a href="https://www.youtube.com/watch?v=edMVvwoOD2k" target="_blank">http://www.youtube.com/watch?v=edMVvwoOD2k</a>

Hi MJM ,Saw this about receivers on the web....   I shall try and and get some info about the Woolf compound with pics soon Got this book about valve gears and events and it is full of good info , but also tells you that you need to compromise with the actually settings quite a lot!!! Talking about Pauls thread on Compounds and efficiency ,one would be more inclined to chat to the firemen that had to shovel the coal !! as well as the M.I.C.E.  experts when drawing conclusions !!..talk to you soon .........

Offline crueby

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Re: Talking Thermodynamics
« Reply #631 on: January 02, 2018, 01:26:39 AM »
That video imay be good in how it shows the piping, I don't know about that part, but the motion at the end was showing a 180 offset, not a 90.

Offline paul gough

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Re: Talking Thermodynamics
« Reply #632 on: January 02, 2018, 05:11:05 AM »
A quick last post before I'm off for about six weeks. Regarding notching up, drivers often start notching up after a few revolutions, especially on passenger trains, though not exclusively. It is very much a save steam and the fireman's back and get the loco into as close to stable demand situation as soon as possible, all contingent on load, grade, railhead conditions and engine condition. Fireman don't enjoy the company of drivers who thrash their engines,ie. run with excessively long cut offs. The complexity of compounding for the most part was its downfall on locos, they were, after all, hugely expensive apparatus to maintain. J. Parker Lamb, 'Perfecting The American Steam Locomotive' P.73, mentions the end for compound rigid frame locos in the U.S. came at the start of WW1 and quotes David P. Morgan, "The bullet that slew it (the compound) was a gadget called the superheater. At one stroke it gave simple engines compound economies without compound maintenance costs." and had the advantage they could be fitted to existing engines. Compound articulated locos lingered for some time more. You are quite correct in thinking it 'mind bending' regarding valve events, when you think of the French compounds running at 4 to 6 revs a second on an express and the driver managing outputs through two independent sets of valve gear it is a marvel, just think of the time any particular port is open! Regards, Paul.

Offline MJM460

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Re: Talking Thermodynamics
« Reply #633 on: January 02, 2018, 11:59:24 AM »
Hi Willy, thanks for posting that video.  Unfortunately my internet is limited at the moment, so I can't  play it, but I will come back to it later, and watch it when I can.

That is an interesting looking book.  A lot of effort was put into studying valve action at the time, there is plenty to learn from them.

I hope that I have not offended you with my comments on efficiency and I see that Paul is thinking on similar lines with his post on life on the plate.  I certainly did not intend to imply that I had any definitive conclusions on the issue.  Like your book says, it's all about compromise.  The theory helps us understand what is going on, so helps guide our experimentation, but in the end, it all has to be proven and the efficiency determined by experiment and testing.  The success of the engines actually built and the experience of the firemen, soon tells which were the best performers.  And in the end, that is determined by the best compromise between the competing issues, thermodynamic efficiency being only one factor, and not necessarily the most important.  Drivability, maintainability, physical size, even cost all come into it, and I am sure other things as well.   

M.I.C.E?  Now I have heard of the institutes of Chemical engineers, and Civil engineers, but which one are you thinking of?

Hi Chris, as I mentioned above, I have not been able to watch the video, so I can't really comment on the 180 vs 90 degree crank angles in the video, and how they fit into the illustration of the place of the receiver in the scheme of things.

Hi Paul, safe travels.  We look forward to hearing all about it on your return.  And thank you for that interesting background on the practicalities of driving those locomotives.  It makes sense when you put it that way, that maximum acceleration might not be the best strategy once the train is moving.  Also a very interesting comment on the superheater killing compounding, as I don't see them as mutually exclusive.   I will look forward to reading about it on your return.  I will send my address in a pm nearer your return time.  I am sure the drivers on those engines would be relying on the tried and tested scientific method of "feel" rather than worrying about valve events while driving.  After all, once the engine has been built, the valve events will follow in turn.  The driver has to determine the best way to operate the engine, of course in conjunction with the fireman.  And it is all affected by the track with its curves and gradients, the load, and so on.

Thank you for all the contributions, and to those who are looking in,

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #634 on: January 02, 2018, 03:22:43 PM »
Hi MJM, So here is my understanding of the steam paths for this engine.....When i first discovered this engine in late 2014 it was as it was when the mill burnt down in 1875 !! They had lifted the cylinder covers but the rest of the engine was all inside the casting so i had to work out what was happening from Intuition  !!. Fortunately my intuition was in top gear !  So....the engine, a Mr Woolf compound with jet condenser has both cylinders connected together from the beam and the valves also connected together from the single eccentric. I had to guess a bit from the outside shape of the casting what went on inside. The cylinders have a steam jacket surrounding them that heats up both cylinders prior to starting the engine. There are no relief valves on the cylinders but a drain cock at the bottom of the larger LP side . The exhaust steam goes directly from the HP to the LP steam chest and then goes down the outside of the casting to the Jet condenser that is operated by a lever once the engine has started. The cylinder sizes are HP 270 mm and LP. 440 mm....I don't seem to have the piston travel dimensions to hand for some reason....  will come back to that. The engine is now being restored and they have started to take it apart so a few pics of that later or you can see them on the  Beeleigh mill construction site on the MEM threads. The engine is rated at 12 Horses power and is original as built in 1830 circa. hope this is of help ....Also M.I.C.E.    Member of the institutionalised contraption engineers ? !!!And no you have not offended me at all ,Just pleased that there is someone out there with all the info to hand...That can put me right !!!
willy
« Last Edit: January 02, 2018, 03:36:31 PM by steam guy willy »

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #635 on: January 02, 2018, 05:48:21 PM »
Hi Paul, just wondering if part of the equation for efficiency had a component of  "the wrong type of snow " and the "wrong sort of leaves on the line" as this sort of thing has disastrous effects on our British locomotives !!! On British locos the inside cylinder Compounds had the eccentric sheaves put on the crankshafts with keyways...so they had to be in exactly the right place (with all the compromises) to work correctly, with no adjustments possible afterwards. so, did they make full size loco mockups to experiment with first ?? Good info here  and a Ib of footplate experience is worth a page full of formulas ,perhaps.

Offline MJM460

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Re: Talking Thermodynamics
« Reply #636 on: January 03, 2018, 12:13:53 PM »
Hi Willy, finally managed to view the video.  I don't like to be critical of people's best efforts especially when they appear to be struggling with language.  But I did not find it very helpful, and many little inaccuracies combined with a poor animation, made it hard to follow.  I think I would go back to Mr Woolf's books.

You have done an amazing job of working out how that engine worked under the casting.  The cylinders are straightforward, they go up and down in phase, the stroke of the LP being longer than the hp due to the differences in the position they are connected to the main beam.  So if one side of the hp cylinder exhausts to the other side of the lp, then steam could be admitted to the hp, then expanded due to the volume changes as it is transferred to the lp, and finally exhausted from the lp.  It is all up to the valve arrangement, and the linkage to the eccentric.

If the valve has no lap, and set at 90 degrees with no lead, I can see it all working with the valves also moving in phase, half way down as the pistons pass top dead centre.  Half way up as the Pistons pass through bottom dead centre.  I am not sure I can get my head around how it would work with valve lap plus lead with the eccentric advanced the suitable amount.  Would it add a little expansion phase to each cylinder?  And how well would the transfer process work?  I think I will hope that someone with CAD modelling skills can whip up a simple (but accurate) model to work this one out in very slow motion.  But again the practical bit is the important part, how did you set your valve positions and the eccentric position on your model?  Did you include any lap?

M.I.C.E, hmmm, I wonder where we all join up?  Glad I did not offend, I am just trying to apply thermodynamics to explain some aspects of how our engines work.  I don't claim any special ownership of the information.  In the chemical engineering circles, it is readily enough available and well understood, and spills over quite naturally into the mechanical aspects of chemical process plants where I spent most of my career.

It might be worth having a look at what thermodynamics tell us about compounding and, now that Paul has introduced it, superheaters, and the reasons it might have killed compound engine advances.  Mind you, I think compounding might have continued for marine and stationary engines, until they were displaced by turbines.  In my experience, these days, steam turbines are available and commonly used as an alternative to electric motors for pump drives when the diversity of power supply is required for reliability.  For example, power station boiler feed pumps are often duplicated, with one electric drive, especially for startup, and the other steam driven so feed water is not interrupted due to a simple power fault.  In process plants, turbines down to under 50 kW are used, though I can't remember the lower limit of the power we considered practical.

It seems a long way back now that I introduced the T - S diagram to show how the thermodynamic properties change in the cylinder of an engine.  I will attach it below again for reference, as it is not very convenient to have to keep referring back a long way.  First let's refresh our memories of what this diagram shows.  The line 1 - 2 is the constant temperature, constant pressure boiling in the boiler.  The sloped curve, 2 - 3, is the constant pressure temperature increase in the superheater.  The vertical line,  3 - 5, or constant entropy, is the ideal adiabatic expansion of the superheated steam to the exhaust pressure.  For adiabatic expansion, the entropy is constant through this expansion, and the change in enthalpy is due to the work done by the steam in the cylinder.  Adiabatic expansion is an ideal process which cannot be achieved in a real engine, but the work done by the steam is the maximum that could be done by any engine, and is the standard by which we assess the adiabatic efficiency of a real engine.  The line 3 - 4 represents the expansion between the same pressure limits in a real engine, it ends at the same pressure but a higher temperature than the ideal engine.  (Remember that line 5 - 4, is the constant pressure line for the exhaust pressure.)

To progress our examination of compound engines, we need to refine that diagram, and show the compound more accurately than implied by the simple line 3 - 4.  But first let's look at the simple superheater cycle.  Without superheat, the engine expansion is a vertical line from point 2.  To understand why the superheater is so important we need to look at the overall thermal efficiency of the cycle without superheat and with superheat.

Now the concept probably sounds a bit complex, so I will break it down to about three steps.  It will also help me get to bed at a reasonable time.  So tomorrow, I will show you how the thermal efficiency of the cycle changes with superheat.  Then I will try and show the differences between that ideal superheat cycle and a more real one.  Finally, I will try and show the compound engine on that diagram and the corresponding thermal efficiency.

Let's think about that much for the moment and I will continue tomorrow.

Thanks for looking in,

MJM460

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #637 on: January 04, 2018, 01:06:43 AM »
Hi MJM , yes i think you are right about the graphics on some of these "helpful" videos...as they are produced on  CAD  some shapes and dimensions are not actually correct.  I have checked my drawings and there is 1/4" lap on the valves as far as i can tell. There is 1/8" exhaust lap on the HP side but no Exhaust lap on the LP side i had to measure the ports whilst inside the valve chests which made it a bit difficult. The piston travel on the LP side is 40 " but i don't know the width of the piston and the HP piston rod is 18" towards the beam bearing from the LP side. The beam end centres are 123".  I hope this is useful and this engine was designed and built almost 200 years ago !! I don't know exactly how much eccentric lead there is as they have only just managed to turn the engine over.
Willy

Offline MJM460

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Re: Talking Thermodynamics
« Reply #638 on: January 04, 2018, 11:25:50 AM »
Hi Willy, I was really intending to ask," how did you set up the valve laps and eccentric position on your model?"  Did you make the valves to exact length, and set the eccentric at 90 degrees, or did you make your valves with a little bit of lap and advance the eccentric accordingly? 

Obviously the beam angular motion is determined by the crank on the flywheel shaft and the distance its conrod  connection point is from the centre pivot.  The arc lengths traced by the connecting rod connection points for the hp and lp cylinders are determined by their distance from the same centre pivot, so clearly a bit more for the lp cylinder. 

Yesterday, I started to break down the steps in understanding why Paul's pioneer would have said the invention of the superheater killed the development of compound engines.

I don't know what pressure those early locomotives would have run at, but just as an example, I assumed 700 kPa (g) or 800 kPa absolute, very close to 100 psig.  Probably more realistic for a model with a heavy load, but it will do for the purpose.  So if we assume that line from 1 to 2 in yesterday's drawing is 800 kPa, for which the steam tables tell us the temperature is 170.4 deg C, we can now look up the enthalpy and entropy of the dry saturated steam, (point 2) and the corresponding properties for the saturated liquid, (point 1 on that drawing.)

If we further assume that the water in the tender which is pumped into the boiler is at 20 degrees C, we can look up the enthalpy of that water and calculate the increase in enthalpy from cool water to dry saturated steam.  It works out to be 2685.1 KJ/kg.  That heat plus the amount that goes up the stack has to obtained by burning coal, which the fireman has to shovel into the firebox.

With no superheater, that dry saturated steam is expanded in the engine to the exhaust pressure of 100 kPa, atmospheric pressure.  Now, just as we worked out in a previous post on an engine test, we can calculate the work that could be obtained from an ideal adiabatic expansion over that pressure range.  Remember the process was to use the second law of thermodynamics, which says for an ideal adiabatic expansion there is no change in entropy.  That entropy is very useful in looking at the performance of engines, and you can see why I had to introduce it quite early in the thread.  When you know the entropy of the exhaust steam, you can calculate the enthalpy, and hence the enthalpy difference which goes into work during the expansion.  The entropy means that the exhaust steam is wet steam, with dryness of 87%, which means the exhaust enthalpy is 2393.9, and the change in enthalpy is 375.2 KJ/kg.

From that we can calculate the overall thermal efficiency of an ideal adiabatic engine as 375.2/2685.1  = 14%

It is important to remember that this is the best performance that can be obtained from an ideal engine, and the performance of a real engine will be much less.  In fact we could guess a boiler efficiency of about 70%, meaning the rest of the energy is lost up the stack, and we could estimate the efficiency of a real engine of perhaps 75% of an adiabatic engine, giving not much over 52% of the adiabatic efficiency for a real engine and boiler.  However all the figures can be assumed as roughly proportional in this type of calculation.

The interesting result of these calculations comes when we continue through to the same calculations for a boiler with a superheater.

When the boiler has a superheater, the superheater is represented by that section from 2 to 3 on yesterday's drawing.  That is the form of the constant pressure line, once you start superheating.

I assumed a superheater outlet temperature of 350 deg C.  Again, I don't know what figure would be more typical, but that will do for our purpose.  To heat the dry saturated steam at point 2 to point 3, an additional 401.6 KJ/kg has to be added to the steam.

When the superheated steam is expanded in our ideal adiabatic engine, the exhaust at point 5. Is also slightly superheated, in this case to 109.4 deg or 9.4 degrees of superheat.  Again, the entropy does not change in our ideal engine so the exhaust enthalpy can be calculated and hence the change in enthalpy during the expansion, or work produced.  When the calculations are completed, the work output from an ideal adiabatic expansion is 466 KJ/kg.  A quick review shows that we put 14% more energy into the steam but obtained 24% more work out put.

If we assume the engine runs on the same route, with the same load, we would expect the work required to be the same, so if we get more work out of quantity of steam we actually need significantly less steam when a superheater is included, and that means shovelling less coal.

Again I have kept emphasising that the calculations are based on an ideal engine, one that the laws of thermodynamics show cannot be exceed by any real engine.  And in fact a real engine will always have losses that mean it produces less work output than that ideal engine.  But it seems reasonable to assume that the losses might be roughly proportional and we would get a similar result if we were able to compare real engines.

Now that is probably enough headache producing exercise for another night, so tomorrow, I will try and see if the laws of thermodynamics can show us the difference in performance between a simple single expansion engine and a double expansion or compound engine.

Thanks for following along,

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #639 on: January 04, 2018, 10:35:45 PM »
Hi MJM , When i took the measurements of the engine sometime ago the engine was unable to turn and the valve rods and components took quite a few twists and turns via several bell cranks before they reached the valves them selves. This photo shows the crank and eccentric in line, sort of.... when i come to timing the model it was done more by dead reckoning than actual measurement. So i did get the engine to run as can be seen from the videos...The way i did it was to make a sheave with an extended boss to take a grub screw, once the engine was running with the sheave in the correct position this boss was removed and a slot cut to line up with the crankshaft.

Offline MJM460

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Re: Talking Thermodynamics
« Reply #640 on: January 05, 2018, 10:58:33 AM »
Hi Willy, with the eccentric approximately in line with the cranks, you can see with the horizontal eccentric strap, the valve would be in mid travel, while the flywheel end of the beam is at top of its travel, hence the pistons at the bottom of their travel.  So basically very close to the normal 90 degrees for a vertical or horizontal engine.  Of course assuming that the eccentric strap is horizontal when the valve is at its extreme positions.  But your tuning the final position, once again is the practical approach.  I like the idea of making the eccentric easy to adjust then modifying it after the best position is found, I am noting that for future reference.  Simple approach to an otherwise frustrating problem.  I trust also that if there was a receiver of reasonable volume, you would have found it.  So it looks like the hp exhaust directly opens to the lp inlet, so the expansion which began in the top of the hp cylinder continues as the underside of the lp cylinder receives the steam into an enlarging volume, and hence contributes output work in the lp cylinder, before being exhausted to the exhaust condenser.  The same process occurs between the steam admitted to the underside of the hp piston, which is then further expanded on the top of the lp piston.  Relatively simple to see, now you have done all the work, but a great effort to get so much information from the machine in its state at the time.

Now I have been trying to work through the differences between simple expansion and compound engines from the thermodynamics point of view.  I have been looking at the engine performance from the view of the adiabatic expansion model.  The reason for this is that the laws of thermodynamics tell us that adiabatic expansion gives the greatest possible work output from the steam at the given conditions.  Any real engine will give a lower work output.  So the first thing is to have a clear understanding of the model.  Basically, the model assumes the mass of steam at boiler pressure, expanded to the exhaust conditions with no heat transfer. 

How does this compare with a real engine?  Well, first, steam is admitted to the cylinder while the inlet valve is open.  During this process, work is done on the piston, the expansion inherent in the work production includes the whole volume of steam back to the boiler, where of course the pressure is maintained by the heat input, but it is only the work and heat transfer in the cylinder that interests us. 

When the valves are shut, the expansion continues in the cylinder, but of course the piston has already travelled through part of its stroke, so there is only part of the stroke remaining, not anywhere near enough to expand the steam to exhaust pressure.  So what happens next.

The thing is that both simple expansion engines and compound engines are different attempts to approximate that ideal adiabatic expansion in a real machine.  They are not fundamentally different processes, just different approximations to the same process.  They are both trying to efficiently extract the work potentially available in the steam.

Yesterday I worked through that adiabatic process for an engine operating at 800 kPa inlet pressure, remember this is absolute pressure, around 100 psig.  With an atmospheric exhaust system.  Before the superheater was invented, saturated steam was expanded and gave a wet steam exhaust. 

The volume of the steam at exhaust pressure is just about 7 times the volume of the inlet steam at 800 kPa.  Way too high for our simple cylinder to accommodate after the inlet valve has closed.

If we assume cutoff at about 50% of piston travel, simply for easy calculation, the volume doubles from cut off to the end of stroke.  From the steam tables we can read that the pressure would be about 380 kPa, not exactly, that requires more interpolation of the tables than I have done for this exercise, but I think close enough for the purpose.  (About 40 psig).  Still well above the 100 kPa atmospheric exhaust.

This is where we see the difference between the simple expansion engine and the compound.

In a simple engine, the exhaust valve is opened, and the remaining pressure lost into the exhaust system.  In a compound engine, the steam is exhausted into the lp cylinder, with or without a receiver in between.  Let's follow the example of Willy's engine, and ignore the receiver for the moment.  The lp cylinder with its larger diameter and longer stroke opens up more volume than is being exhausted by the hp cylinder, so there is a net work output in the lp cylinder as the steam continues to expand to the full volume of the lp cylinder, before finally being exhausted to the exhaust system at 100 kPa.

So the issue comes down to how much work is produced in each engine, and preferably which real engine design produces more work from a given quantity of steam.  In other words, which is the most efficient.

I suspect that as good a way to look at the difference between these two ideas is to draw an indicator diagram for each, or probably more accurately, a P - V diagram for each engine cycle.

I have put some thought into how best to draw this, and am not quite there yet.  I hope tomorrow, but it is predicted to be over 40 deg C here, and no air conditioning.  So I am not sure how much I will achieve.  Might be a very short post, but I will at least check in.

Until then, thanks again for following along,

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #641 on: January 05, 2018, 03:39:15 PM »
Hi MJM,  + 40 in Aussie and - 40 in USA  so is the climate in balance ?? So when this engine was made they were still experimenting with the technology. On a later Triple they had 3 pressure gauges presumably to record the 3 cylinder pressures ? On the Beeleigh there are holes drilled through the cylinder caps and it is likely that they had a pressure gauge attached to show what was happening.? These holes also had a double valved oil reservoir to introduce oil into the cylinders at periodic points.   Also is it possible to design an engine that has zero pressure  Atmospheric at the end of the LP stroke ? or is it advisable to have some back pressure as in IC practice ? There is a sister engine at the Ramm brewery that is still running that has a few modifications to it.....Also is there a graph /table that shows the introduction of technical terms over the last 300 years ?? Some more homework for you i'm afraid !!! The Ramm engines have also been insulated with Mahogany slats !
« Last Edit: January 05, 2018, 03:44:51 PM by steam guy willy »

Offline MJM460

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Re: Talking Thermodynamics
« Reply #642 on: January 07, 2018, 12:02:49 PM »
Hi Willy, looks like the average is zero.  I suppose that is the case somewhere.  Three pressure gauges almost certainly for the three valve chests or cylinder inlet pressure.  These pressures are not discretionary, but inevitable from the relative cylinder volumes.  As mentioned earlier, the best efficiency is obtained from equal pressure ratio in each stage.  If the second stage cylinder is too big for this, it will accept more steam, and hence lower the interstage pressure.  If it is too small, it will not accept all the steam from the hp cylinder unless the pressure rises a bit.  So the eventually settled pressure is determined by the relative cylinder volumes.  Similarly for the third cylinder.  If the interstate pressures start to drift, it may indicate that valves are passing, altering the capacity of the cylinder, so those gauges would be very useful to the engineer.

Fluids only flow from a higher pressure to a lower pressure.  If the pressure is uniform everywhere, there will be no flow.  So when the exhaust valve opens, the pressure in the cylinder has to be higher than outside to make the steam flow through the valve.  If the pressure is too low in the cylinder, steam from the exhaust will flow back in until the pressures equalise, then the piston trying to 'squeeze' the exhaust out will cause the pressure in the cylinder to rise until the necessary flow occurs.  The pressure at the start of the exhaust is not discretionary, but necessary due to fluid dynamics.

If you want the cylinder to have zero gauge pressure at the end of the stroke, say 100 kPa absolute, then you would need a condenser to lower the exhaust system pressure enough for the exhaust steam to flow out through the valves.  Then of course you need a condensate pump and an air pump, so you might as well make them all sufficient to make the vacuum a bit more useful.

As for the homework, surely if such a table or graph exists, surely it will be hidden in your library somewhere.  It is certainly not in mine, unless of course it is in that book by Professor Jamison, but I have not noticed it.  But it is the only historical book that I have.

By the way, sorry about last night.  Not only the end of a very hot day, but I must have chosen the the time that Ade was doing the maintenance.   It has to be done, and it is sure to be the wrong time for someone on a world wide forum.  It has given me time to improve my posts little, I hope.

Forty two degrees they say here.  You might wonder why we don't get acclimatised to it.  You start to if you get more than two weeks in a row, though you don't really get fully acclimatised to those temperatures.  However, Friday was about mid twenties, as was today.  You don't get acclimatised to a one day scorcher.  That is our weather pattern.

I have been looking in detail at compound expansion.  The T-S diagram that I use to determine the work done by an ideal adiabatic engine does not easily show the difference between a compound expansion and a simple expansion engine.  I tried a simplified picture of an indicator diagram.  You know the type produced by a special instrument as part of engine monitoring.

In a real indicator diagram, the corners are all rounded due to the throttling effects during the finite opening and closing time of the valves as we have previously discussed.  In idealised diagrams often produced in text books or other articles, the corners are more square, just to show the principles clearly.  The area in a plot of pressure vs. volume is the work done by the cylinder and can be extended to the power by the engine.  The rounded corners all reduce the actual work done, but square corners make the area of an idealised diagram easier to calculate.  I have even avoided including the compression phase, which again reduces the calculated work done if they are included.  But the simplification allows easy calculation and comparison of the two cycles, so is appropriate for the present purpose.

In the attached hand drawn diagram, I have included two cycles.  On the left is the simple cycle, exhausting to atmospheric exhaust.  The area with the cross hatching represents the work done through the whole cycle.  For the calculations I used the pressures from a few days ago, and drew the diagram for an hp cylinder volume of 1 m^3.  So the pressure times volume is a measure of the work out, proportionally smaller for a smaller volume engine.

On the right is the compound cycle.  The pressure ratio being similar for each stage gives 283 kPa for the interstate pressure.  I have taken the liberty of using 280 kPa in case I need to go to the steam tables, to minimise the amount of interpolation required.  I have assumed the volume of the lp cylinder is 1.7 times the volume of the hp cylinder.

In both cases I have assumed the initial cut off at 50%, so the volume ratio during the expansion is 1:2.  The steam tables are not very convenient, but are the accurate model to determine the resulting pressure at the end of the expansion.  It turns out that the 800 kPa steam expanded to double the volume gives a pressure of about 380 kPa.  Again, I used 375 kPa so as to have the figures without interpolation.  But it still requires a trial and error method.

You can see that the calculated result of all this simplification, about 20% more work output from the compound engine.  Not a figure we can totally rely on for accuracy, but almost certainly in correct proportion.  I have overlooked the effect of the volume of the transfer pipe and valve losses and so on.  But surprisingly similar to the extra work output from the superheat cycle I calculated a few days ago.  Obviously a lot simpler than resorting to compound engine and so much simpler to maintain.  Just as that pioneer said.

The part I do not yet understand is just why we do not use both superheat and compounding.  That would seem to return the advantage to compounding.  Though compounding still leaves us with the problem of starting at any point in the rotation.  I wonder if anyone else can offer some clues.  It is a pity that Paul is away at the moment, he may have some answers.

By the way, the comparison of the hp stage of the compound cycle with the simple cycle shows very clearly the effect of exhaust pressure.  For the simple cycle, with the exhaust pressure assumed atmospheric, the negative work from the exhaust cycle is that area under the the horizontal line at 100 kPa.  For the hp cylinder of the compound cycle, the exhaust cycle negative work is the area under the line at 280 kPa.

For both cycles the positive work from the power stroke is the area below the top line horizontal at 800 kPa for the first fifty percent of the stroke, then the curved line representing the pressure during the expansion, right down to the zero line.  The cross hatched area is the resulting positive work output of the cycle.  The steam is expanded to double the volume it occupied at 800 kPa.  It only expands to 380 kPa, regardless of the exhaust pressure.  The pressure is then throttled through the exhaust valves to only a little above the exhaust pressure.  This is all easy to see in the simplified diagram.  If we round the corners to more accurately show a real engine, it tends to obscure these principals, but the process is still as I have described.  The corner rounding reduces the positive work from the power stroke, and increases the negative work from the exhaust stroke, so reducing the net work output.

You can see the difference exhausting at 280 kPa instead of 100 kPa.  You can extend this to a condensing cycle where the exhaust pressure is significantly below 100 kPa.  There is advantage in power output to a condensing cycle, even when there is no further expansion, due to the reduced negative work of the exhaust cycle.

You will also notice that I assumed an early cut off.  I don't know if the valves can actually be arranged to achieve this.  However compound expansion engines are often fitted with Stevenson's valve gear so I assume the cut off is achieved in a similar manner to a simple engine.  Just for interest sake, I did the calculations assuming constant pressure for the whole cycle, another variation of the simplification, but the results were in similar proportion.  I expect this would also apply to in between points of cut off.

I hope this has clarified the compound cycle and how it is different from a simple expansion.  I will await the resulting comments and questions with interest.

Thanks for following along.

MJM460

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

Offline MJM460

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Re: Talking Thermodynamics
« Reply #643 on: January 07, 2018, 12:08:42 PM »
Whoops!  That picture is upside down.  Not sure how I did that.  I hope you can still follow it.

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #644 on: January 07, 2018, 12:42:47 PM »
Hi MJM Ok Done

 

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