Talking Thermodynamics

[MJM460]

Thanks, Willy.  I hope the diagram makes more sense now with the text now.

MJM460

[MJM460]

Thanks again, Willy, for turning that diagram around.  It is much appreciated.

I hope that no comments means the post was perfectly clear, though I am not convinced.  But I thought there were a couple of points that could do with some further explanation.

First the units of work.  I used kPa for pressure and m^3 for volume.  Using Pascals of course does obscure the fact that a Pascal is the same as a Newton per sq m.  So kPa is the same as kN/m^2.  When this is multiplied by the volume in m^3, the units for work are kN.m.  If I had used a more realistic cylinder swept volume of one litre, then the units of work would be N.m, much more suitable for a model.  This calculation of the work output of the cycle is the same as the calculation of work from an indicator diagram, though the more complex shape of a real engine diagram means that the area must be calculated using either graphical methods, or a planimeter to measure the area.

Another thing you may have noticed was the increase in volume of the steam during the expansion.  A volume of steam equal to half the hp cylinder volume, occupies 1.7 times the volume of the hp cylinder by the time it has been expanded in the lp cylinder, so an expansion of 3.4:1.  If the  engine is equipped with a condenser system to extract even more work, the volume keeps expanding, so that a very low pressure cylinder has to be very large.  We can get more work out of the steam by expanding it to a lower pressure, but at the expense of requiring very large cylinders.  Alternatively you can use other methods of handling the large volume, such as those turbines on Titanic.  All a delicate balancing act between power output, efficiency, and cost.

The calculations have been based on a double expansion, with a pressure ratio of 2.8 across each stage.  If the same 800 kPa steam is expanded in a triple expansion engine, the ideal pressure ratio over each stage would be the cube root of the total pressure ratio (800/100 = . The cube root of 8 is 2, (2 x 2 x 2 = so the pressure ratio over each stage would be 2.  The cylinder volumes would then have to be sized to give interstage pressures of 200 kPa and 400 kPa for the supply steam at 800 kPa and exhaust of 100 kPa.  The cutoff would have to be limited so the first stage expansion did not result in a pressure lower than 400 kPa, in fact it has to be a bit higher to enable the exhaust steam from the hp cylinder to flow to the next stage.  Similarly for the second and third stages.  Once again we see that those cylinder volumes and interstage pressures are not really arbitrary, but determined by the steam inlet and exhaust pressures Anne the number of stages.

It was mentioned earlier that some engine designs use a receiver between stages.  When the exhaust of one cylinder passes into the fixed volume of a receiver, the pressure rises, while when the steam passes from the receiver to the next stage, the pressure falls.  Like any other interstage pressure, the receiver quickly settles to a pressure level where the mass of steam from the higher pressure stage is exactly equal to the mass of steam taken by the lower pressure stage.   If the receiver consists solely of the transfer pipe, it would be necessary to have the inlet and exhaust valves of the cylinders right in time, otherwise very high pressure fluctuations would occur in that transfer pipe.  While if the receiver is quite large, pressure fluctuations would be much smaller.  I have to conclude that the purpose of the receiver is to accommodate differences in valve timing which I assume would be inevitable once the driver starts to notch up the valve gear to reduce steam consumption as the train gets moving.  Working out the valve timing for variable cut off by hand calculation feels a bit too hard these days when computer modelling techniques are available, so I will give that a miss.

I am not sure that there is much more I can say about compound expansion.  I hope that little introduction has been both interesting and useful.

Any ideas on what you would like to look at next?

Thanks for looking in,

MJM460

[steam guy willy]

<a href="https://www.youtube.com/watch?v=2EkjRslFgSM" target="_blank">http://www.youtube.com/watch?v=2EkjRslFgSM</a>

Hi MJM ,  So how did early designers decide on the dimensions  of the cylinders for Compounds and later Triples ?  And here is an electrically heated steam crane i made some time ago... i could do a heat up graph for this soon if it still works ?!!! Thanks for all the info you have provided and I was wondering how much Fluid dynamics and thermodynamics overlap. Also my thermometer is quite inaccurate as when i tried to take my temp it only registers 92/93  rather than 98.4 !!! it did mention on the blurb that it was only about 3/5% accurate  !! but how much this would vary at higher temperatures is unknown ?!!

[MJM460]

Hi Willy, I am not sure of the time line, perhaps your library has some answers on that.  So I don't know if understanding the theory lead to development of compound expansion designs, or if the theory followed later.  I have previously spoken in praise of the intuition of those early pioneers, who achieved so much well in advance of the developing theory.  They may well have been led by intuition to build a compound  engine in the search for more efficiency.  In this case, they may not have had much idea how to size the cylinders, it could even be affected by the inaccuracies in those tables you have pointed out before.  They may have started with something as simple as reconnecting the steam to a two cylinder engine to see if there was advantage in expanding the steam twice.  You see, the interstage pressure will find its own level, depending on the relative cylinder volumes as I have explained in the last few posts.  So you can build an engine with any relative cylinder sizes and it will work, it is just that this may not be the most efficient cylinder sizing.  Finding the optimum interstage pressure level and relative cylinder sizes for maximum efficiency and power output may have come later.  Another case where combining history with theory makes the whole study more interesting.

I love that little crane.  Is that based on one in a book, or your own design from a historical prototype?  If you want to do a heat up curve, I will help you through the calculations.  It will be interesting to see how it compares with the horizontal boiler.  If you have a boiler drawing, it will help with calculation of the mass of copper.  If you can measure the resistance of the element, that will reduce another source of error.  I assume the insulation is just those wood strips, or do you also have an insulation layer?  But surely this does not mean you have run out of questions!

Fluid mechanics and Thermodynamics.  I feel that subject titles are an indication of the central emphasis.  However, at the boundaries, it is difficult to draw clear lines.  For example, in convection heat transfer, the temperature gradient is determined by the fluid flow, and the velocity boundary layer.  But the flow is influenced by the fluid properties of density and viscosity, which both change with temperature.  So the temperature gradient affects the flow, and the flow affects the temperature gradient, you can't separate the two.  Even if we confine the heat transfer to solid conduction, well solids are only liquids whose temperature has fallen below the freezing point.  Though some solids break down chemically before they melt if you try and heat them.  So there, and also in dealing with combustion heat sources, you rapidly get mixed up with chemistry.  This thread could not be written without a language subject, and geography affects ambient conditions, history determines how much knowledge has been accumulated for you to build on, and explains things like development of motor cars, pneumatic tyres and so on.  So no clear boundaries.  And you can't run a hydrocarbon processing plant without an understanding of fluid mechanics, so don't feel that questions have to be limited to one area.  As always, I will say if I don't know.

Thermometers.  Quite a range of subjects today.  Hmmm, if your body temperature is only 92/93, perhaps you should see the doctor, if it is not too late.  I assume you put the thermometer under your tongue for a reasonable time in the normal manner.  Some authorities say that putting it in the other place is more accurate, but don't break it.  Under arm is often used for babies, but I suspect it is a less accurate method.

The thermometer accuracy depends not only on the temperature at the bulb, but the stem temperature also has an influence, and for best accuracy, there is a stem correction that has to be taken into account.  I have not done this since high school, but Mr G should be able to tell you how to do it.  It is also determined by the accuracy of the capillary.  If the diameter is not accurate to the intended value when the scale was engraved, the reading will be a constant percentage out, and you could make a calibration curve by calibrating at only two different temperatures.  The ice point and boiling points are good points to start as temperatures you can reproduce at home.  However, if the thermometer is poorly made, so the diameter of the capillary varies along the stem, then the accuracy will vary with temperature and you would need to calibrate by comparing with a more accurate thermometer at several temperatures over the range you want to use.  It might be possible to check the consistency of diameter with a low power microscope with a scale, perhaps one of those computer ones that are readily available these days.  By the way, I hope we are not talking about that good quality thermometer with the certificate you showed us previously.  In that case, it is important to very carefully calibrate before you complain. 

While the ice point and boiling point are accurate reference temperatures, it is sometimes difficult to get your temperature instrument to show them accurately.  The boiling point does depend on atmospheric pressure so you need to check the atmospheric pressure.   Again, Mr G will find the official bom reading in your area for you.  The ice point is even harder.  You need an insulated container full of small ice blocks or even crushed ice made from very pure water and minimum water, all well stirred (not shaken).  I am not sure how much the freezing temperature of potable water varies, but impurities change it and if your water is particularly hard, it may vary a little.  The stem correction may be another factor.  Body temperature is a little harder to measure with the same accuracy. 

As always, accurate readings are simple in concept, but sometimes more difficult in practice, you can only do your best with the procedure, and try a few repeat measurements to get an idea of variability.  Essentially you have to minimise any temperature differences throughout the fluid you are measuring, and minimise any heat gain or loss to the stem, and give time for everything to reach uniform temperature.  But the readings at ice point and boiling point give a very good idea of the accuracy of your thermometer.  I hope that helps.

Thanks for following along,

MJM460

[MJM460]

I have two small Meths fired boilers and I keep promising myself that I will conduct some heat up and cool down tests on them.  The excellent job that Willy did for his electric boiler put me to shame, and inspired me to finally get a round tuit.  Everyone needs at least one of those.  So in the holiday period after Christmas, I finally did some test runs. 

It was a bit of an adventure, I suspect it always is, when a model has sat for a while and not fired up.  I have been setting up a spreadsheet to see if I can do similar calculations to those I did on Willy's boiler.  Obviously the big difference with a fired boiler is that part of the heat is lost in the flue gas, but I want to see how much of the heat from the fuel burned can be accounted for in the water and the copper shell. 

The first one is a simple pot boiler from 1 1/2 inch copper tube with torispherical ends.  It sits on a stainless steel firebox, and is open at the top, similar to the little Mamod units.  Not much use for insulation on these, as the flame licks pretty much the whole boiler apart from the ends.  Perhaps I could insulate those.  The steam outlet is taken from a banjo type fitting under the safety valve, and curls back under the boiler and around the firebox before out to the engine.  The engine is actually driving a small generator, which has not yet had a load connected.    The generator is a small 280 size brushed DC motor.  When the engine runs at about 1000 rpm, the motor produces an open circuit voltage of about 1.3 V.  The short circuit current read about 0.3 amps before the engine stalled, clearly needs a bit more steam pressure to keep it running.  I think I should design a load to draw about 0.15 amps and try again.  The drive belt is a simple rubber band, and the pulley sizes mean that the motor is turned at about 3000 rpm.  Still very slow compared with its no load speed as a motor, or even it's loaded speed, hence the low voltage.

I will try attaching a photo, I think I have it small enough to attach.  Otherwise I will have to try again tomorrow.  Stealing time during a beach holiday to do the calculations, and only part done at the moment.  So instead of writing, I will continue with the calculations, and hope to have some results to publish tomorrow.  So just a short post tonight.

Thanks for looking in

MJM460

[steam guy willy]

hi MJM, that looks quite an interesting engine , is the doubled back steam pipe used as sort of superheater ? there is quite a lot of brass on the fittings  that would make a good radiator ! there are also quite a few odd parts attached that seem to have nothing connected to them  ? is this all original and has it evolved over time via different makers? Is it also floating in a pool?  I checked my new thermometer with some older mercury thermometers graduated in degrees Celsius and there is 1 degree different.

[MJM460]

Hi Willy, yes the steam outlet doubles back into the furnace as a superheater.  Made from a 450 mm length of tube, a bit over a full turn around inside the furnace casing.  Heats steam from 110 deg (143 kPa absolute) to 127 C so quite effective for a small model.  Perhaps I should make a new one from a 1000 mm length to see how it affects overall performance.  You are quite right to observe that all those brass fittings probably loose a lot of heat from such a small model.  I have often thought I should try wrapping them with that silicon tape.  But first a few more runs to establish a base line performance, so I will be able to see how much difference it makes.

Everything is connected and almost steam tight as shown.  Almost, as I found some of those fitting nuts were too long, so would not tighten quite enough.  They have now been touched up with a file and a milling cutter and I think I have a new run proving them totally tight.  I think I must have mixed them up before assembly, and they are obviously not interchangeable.

A few points that might be confusing you:-

The filler plug is also a thermowell that I have shown previously in pictures.  The solid brass plug protrudes about an inch into the boiler, but the hole you can see is is only drilled 7/8" deep for the thermocouple, (not fitted in the picture), so it does not penetrate into the steam space.  Drilled 3 mm diameter, so all my thermocouples fit.  The safety valve is on top of a banjo fitting for the steam outlet.  The safety valve has the straight through passage unobstructed, the steam outlet is the side branch.

The 90 degree elbows are combined with thermowells for the engine inlet and outlet thermocouples.  The horizontal bend on the inlet means only a very short thermowell, the exhaust one allows a longer thermowell, so probably gives more accurate reading.

You can also see the displacement lubricator in the background, with the oil plug on top and the white hand wheel. 

The engine is actually my second engine, double acting, with flanged cylinder heads and a screwed gland, built with the same frame dimensions and the same 12.0 mm bore as the first which was single acting, see my avatar.  With identical frame dimensions, it is interchangeable in the steam plant, but obviously a bit more power output if I can keep up the steam pressure at the higher flow.

The two little threaded holes in the top of the frame are the ends of the vertical steam drillings and are plugged with 3 mm grub screws.  Probably rusted in by now.  The little screwed fitting on the side is a warm up valve.  When opened, it connects the inlet and outlet steam drillings, allowing condensate to be blown through to the condensate separator during startup, with a little steam flow to warm the frame.  Then I close it while the engine runs.  I am still learning to make small hand wheels, I need to revisit that one.  The piece of white tape on the flywheel rim is the reflective tape for my optical tachometer.

The Meths burner sitting beside the boiler is also reflected in the stainless furnace casing, where you can see most of the fuel tank.  Unfortunately the filler plug with a tiny vent is just out of sight in the photo.  The join in the fuel line was an attempt to make the tanks interchangeable for different burners, but I would be better to get more confident at bending up and silver soldering the tanks, and just make a new one for each burner.  The "wick" in the centre part is actually cut from a porous water filter element, not sure if it is clay or ceramic.  There are little tongues of blue flame from the holes in the two side sections, the whole thing being an attempt at a semi vapourising burner.  Another area for further development.  The steam separator chimney exhausts essentially dry steam, while some oily condensate discharges from the gooseneck in the base of the separator.  I collect the condensate with an empty tin that fits under the outlet.  I have previously described the separator.

The boiler is my own design.  I turned the plugs to form the torispherical ends, a form that has just two radii, but approximates the semi elliptical form, and much easier to make.  Fully code compliant, it avoids the need for staying of a flat end.  But next boiler I make will have a central stay to make it easier to hold the ends in place during soldering.  But I will still use the torispherical form.  Had a bit of help with the soldering, but at least I made all the parts, and did the pressure test.

The "wood" base has a channel cut in under the furnace box to allow the burner to be placed lower.  It was initially too close to the boiler.  It is easily packed up, to allow experimentation with the burner height.

It is all "floating" on a glass topped table in our garden.  The glass surface is textured, and now you mention it, it does look rather like water. 

I know it is not up the the normal standard for this forum, but it was my first effort.  Definitely more of a test bed than a piece of art, but I can only get better with all the tips I pick up reading the amazing builds from you and so many other forum members.

I hope that you will now see my first attempt in slightly better light.

Always a pain when the thermometers don't all give the same consistent reading.  But you can allow for a known error.  Next test is to determine which one(s) are correct.

I think that is enough for one post.  I should have some of my calculations ready for tomorrow.  Beach weather is expected to include large hail stones!  So perhaps some indoor time.

Thanks for looking in,

MJM460

[steam guy willy]

Hi MJM , Ok all is explained now and very clear , and ready to go with perhaps lots of areas for improvement with lagging to show how effective this can be !! Does all the steam escape from the exhaust 'Chimney' or can you collect all the exhaust water with the little overflow curved pipe to show how much is used ? It looks like a well thought out arrangement to get interesting results. You mention the white tape for a tachometer .... on my engine i inserted a magnet on the fly wheel and used a cyclometer to get a reading of miles /hour.!! these can be recalibrated for wheel diameter to show "With cunning calibration" RPM  i think.? I have also drawn in the thermowell places on you photo !! please forgive me if this is an unsolicited addition ...but it is quite easy to do this on my apple pooter !!

[MJM460]

Hi Willy, I am glad that my little steam plant is clearer now.  Not as beautiful as your models, but works ok and is set up to do some exploration in thermodynamics.  I am pleased with it as my first attempt.

It would be quite hard to apply some insulation, except perhaps for the boiler ends, and some of the steam piping, as the flame must be allowed to heat the vessel shell.  You can see the similarity with the little Mamod style, but perhaps a top to the furnace casing and a chimney would help reduce the losses to the atmosphere.

The exhaust steam mostly escapes from the separator chimney.  I say mostly because when the boiler first starts steaming, there is a dribble of condensate from the gooseneck, but this soon stops when the piping, engine and separator are all warmed up.  The water that is collected is quite oily, demonstrating that the lubricator works, at least at some stage.  Over what period is another area worthy of some more experimentation.  It's simple enough in principal, but making sensible measurements of such small quantities is not so easy.

The optical tachometer is quite good for an instantaneous reading of rpm as it does not add any load to the engine, and it shows how much an ungoverned engine speed varies over a run.  Your cyclometer is a good idea.  I find it hard to believe that it would add a measurable load, though it is in fact a tiny generator.  But with some cunning calculation, it can be calibrated to measure total revolutions.  For rpm, you would have to time sections of the run, and calculate the average rpm over each time period.  More importantly, the total number of revs an be multiplied be the engine displacement to measure the total steam through the engine.  The collected condensate and the water remaining in the boiler afterwards allow separation of the initial water fill into steam through the engine, steam used for heating up the engine and piping, and that remaining in the boiler.  So both instruments are actually quite useful.

Thanks for marking up the photo, a good way to ask a very clear question.  There are actually only three thermowells, the filler plug, engine inlet and engine exhaust.  The fourth point you have indicated is the adjusting nut on the safety valve.  It is where the stem would protrude if it was long enough.  My skills at turning a thin spindle let me down on that first attempt, so it is not as long as it should be.  It would be better longer so it could be more easily lifted with a pair of pliers to prove that it was not stuck.  I have to remove the valve occasionally with this stem length.  It is an area I could now improve by making a new stem, as I am doing better on those these days.

I learned from doing the calculations I did on your electric boiler the impact of the time between actual full degree temperature changes on the thermometer, and the exact timing of the readings.  So I adopted the method I suggested for you to try in future, I used the iPad stop watch to record a lap time for each reading.  I also found that I had a temperature meter which has a resolution of a tenth of a degree.  Resolution is not the same as accuracy, and I am not pretending that it is that accurate.  But as the same instrument has two thermocouples that read the same when placed close together, I suspect that temperature differences and changes are quite consistent.  More importantly, by watching the tenths increase, I get a good warning of when the whole degree will turn up, so the time when I tapped the iPad could be more consistent.  The iPad records with a resolution of 0.01 seconds, but my reactions are not that good.  I transferred the readings to my log book after the run, but rounded them to the nearest whole second. 

Apart from a few random speed measurements and periodic monitoring of the steam temperature in the boiler and at the engine inlet, I only recorded the time from the engine starting, and the time it stopped.  Boiler pressure and superheater temperature stayed quite constant during most of the run.  I then started recording the cool down time starting from 82 degrees in the boiler.  When the engine stopped, and I removed the burner, the boiler cooled to 82 quite quickly, so no readings for the initial bit.

The tiny boiler heats up quite quickly, so it felt like it was all action.  Much easier with full size equipment where temperatures take a lot longer to rise.  I copied all the readings into a spreadsheet, and calculated the time differences with a formula copied down the column, to eliminate silly mathematical errors.  The spreadsheet was then used to draw the graphs for heat up time and for cool down time.  I have attached a picture of the graphs for heat up time and for the cool down time.

You can see that the method of taking the readings resulted in much more even curves.  I was quite pleased.  Initially, it looked like an irregularity had crept in, but when I checked carefully I had made an error in transcription of one of the readings.  I corrected the error, and the results shown in the graphs are exactly as I recorded them. 

You can see towards the end of the heat up, a fall off in the rate of temperature rise, much as with your electric boiler.  My observation was that there were a few steam leaks in the piping that I spoke of earlier, that most likely explains that one.  I have fixed those now, I hope, and I have two more runs, well one anyway, but that is another story.

This post is getting long enough, so I will have a closer look at those graphs and what they tell tomorrow.

Thanks for following along,

MJM460

[steam guy willy]

HI MJM, intersting observations there ...and the cooling graph only goes down to 30 degrees ,  so is that the ambient temperature where you are at the moment ? It is also very much more linear than the heat up curve. Also only 36 minuets rather than 18 hours !!  On the heat up part it is also quite quick 8 minuets . So the next job is to work out how much energy is required to get to this temperature. also a good analogy between our boilers would be your 'Haystack' and my 'lancashire' type of boiler.I would like to see what sort of thermocouples you actually use as well with a picture ? also if you have more thermocouples you could place them at different points above and around the boiler ... Also you could use some of the shiny stainless steel to reflect back some of the heat with a shroud, until it heats up and radiates even more heat. I was with a friend recently with an old cast iron open fireplace and was quite amazed at how hot the whole fireplace surround was and giving off radiated heat.!! So We have radiation ,conduction, convection and also reflection of heat happening here..Also the accountants in these engine establishments must have been horrified at the amount they had to pay for fuel !! Also saw this about flues...

[steam guy willy]

HI MJM , still thinking about fuel for boilers and remembered that some of those early meths powered 2.5" gauge locos were still able to do passenger hauling on garden tracks

[MJM460]

Hi Willy, yes, I only followed the cooling temperature down to 30 degrees.  The ambient was about 21, and you can see the times were getting longer and the need to keep watching the temperature so closely was testing my concentration.  Obviously the uninsulated boiler cools much faster than your insulated electric boiler.  As would any boiler with a flue for firing, even a centre flue type with insulation on the outer shell.  I suspect the initial cooling down to 50 or even 60 is probably the most informative.

Only 8 minutes to heat up mostly reflects the fact that there is only 130 g of water in the tiny boiler, just a simple pot with no water tubes.  With enough fuel being burned it, can heat up quite quickly.  But that should show up in the energy calculations which obviously come next.  Well, next after your other questions.

So is the simple pot boiler called a haystack?  I have heard the term before but not sure which type of boiler arrangement was being described.  I will also be interested to see the performance of your Lancaster boiler, the more different boilers we can compare, the better. 

I have attached a picture of one of my thermocouples.  You can see it is used with a fairly ordinary multimeter for the readout.  The thermocouple is just that little dot of weld metal joining the two wires at the end of the blue heat shrink.  It is the joining of the two special wire compositions that results in the voltage output when the junction is heated.  It is known as a type 'k', for which the specification ties down the copper and constantan wire, and the voltage - temperature characteristic is also defined in the standard.  Unfortunately very low voltage and not linear with temperature, so possible, but not easy to make your own instrument,  I think the photo might also have been in a post around 11 July 2017, or shortly after.

A few comments about radiant heat.  Those reflections are light being reflected in the same way that radiant heat is reflected.  The only difference between radiant heat and light is the wavelength.  When radiant heat falls on a surface, there are three possibilities, it is absorbed, it is reflected, or it is  transmitted through.  Most surfaces there is some combination.  It is obvious for most surfaces other than glass and similar, that transmission is zero.  Your black cast iron fireplace, mostly absorbs the heat, the dull black surface is the clue, while my shiny stainless steel mostly reflects the heat, just as it reflects light.

When your cast iron fireplace surround receives radiant heat, it absorbs most of it and a tiny portion is reflected.  The absorbed heat makes the iron hot, and as the temperature rises, it in turn radiates heat, proportional to its absolute temperature raised to the fourth power, and with a range of wavelengths, just like light, and most heat at a wavelength which also depends on the temperature.  Eventually it gets hot enough that the amount of radiated heat is equal to the amount of heat received, and the temperature stops rising.  At this stage it is quite hot as you have observed.

When radiant heat falls on the shiny stainless steel surface, most is reflected, however a tiny proportion is absorbed, and obviously none is transmitted.  The absorbed heat means that it gets hot, and starts radiating, both back to the heat source, and also to the atmosphere from the outside.  And eventually the radiant heat loss equals the heat received and the temperature stabilises.  However much less heat is absorbed than if it was a black iron casing, so the temperature stabilises at a lower temperature.  Still hot enough to burn your finger though.

The spiral corrugations are interesting.  When external pressure pushes the ends apart, it tends to try and untwist, but that is resisted by torsional stresses in the outer vessel shell.  Clearly stronger axially than the conventional circumferential corrugations, but I am not sure how much pressure it would support without additional longitudinal stays.  I just don't know.

Heat from Methylated spirits is just as good as heat from anything else, though the flame temperature may be lower than that of gas or coal.  However the main issue is burning it at a great enough rate to provide the steam you need.  It is all about the burner, plus of course sufficient heat transfer area.  In those 2 1/2 gauge locos, I suspect they would have some form of vaporising burner, and I would be most interested to see the design.

The starting point for the energy calculations on my little boiler is the quantity of fuel burned.  I see from my notes that I poured proximate lay 32 ml of liquid with a mass of 25 g.  I suspect that I really need a scale with a resolution of 0.1 g, as the whole gram introduces too much error, about 4%.  It is probably OK, but does not leave much room for other errors to accumulate.  I could use more Meths, but then I would need a bigger boiler, so as not to run it dry before the flame died.

Now I have always used 26,000 kJ/kg as the lower heating value for Meths.  I know in our recent discussion, ethanol was quoted as 29,000.  I don't know if this is just different sources, or whether the difference is due to the effect of the 5% water normally present in meths.  The water has to be evaporated and heated to flue gas temperature, and I suspect this may explain the difference.  I will try some calculations later.  But using 26,000 for the moment, 25 g means 650 kJ of heat released.

The burner was alight for a total of 10 min 42 seconds, of which 7 min 21 sec was the heat up time.  That means it was alight for 1062 seconds.  We can multiply 650 x 1000 to get J/s, then 650 x 1000/1062 gives 612 Joules/s, or 612 watts as the average heat rate during the whole run.

Now just as the electric element changed resistance as it heated up and hence changed the rate of energy input, the burner does not really burn at a very uniform rate.  My burner tends to start off a bit slow, rather like a simple wick, then there comes a point where some vapour is produced and the blue tongues of flame appear at the row holes down each side of the burner.  This seems to increase the heat output.  This is an additional complication on top of the obvious very significant heat loss with the flue gas.  Also, when the burner is first lit, the boiler and its water is cold, so there is a bigger temperature difference between the flue gas and boiler shell at the start than later when the boiler is up to steam temperature.

This is where I copied Willy's idea of measuring the temperature and time during heat up, it means the boiler heat input can be calculated every 5 degrees interval during the heat up, and I believe the graph of the heat up time energy input will show the increase in heat output, but that will have to wait until tomorrow, when I will try and lead you through the method I use to do the calculations.

Thanks for looking in,

MJM460

[Dan Rowe]

So is the simple pot boiler called a haystack?  I have heard the term before but not sure which type of boiler arrangement was being described. 

MJM, here is a thread about haystack boilers:

http://www.modelenginemaker.com/index.php/topic,6900.msg142585.html#msg14258

Cheers Dan

[steam guy willy]

Hi MJM, so ,some info about Haystack boilers has appeared on a new thread , and here are some pics of the Lancashire type of boiler.....I was also wondering where fair comes between ?! on the insulation chart ? Also does lit meths give off more heat if the ambient temperature is warmer. Also with thermocouples it says to calibrate them use ice at atmospheric pressure .....if you have a container with ice in it and compress the air will it melt at a higher temp ? Does compressed ice in a glacier behave in a different way ? can you compress ice ?

[MJM460]

Hi Dan, thanks for that article.  It suggests that my properly code designed horizontal cylindrical boiler is not a haystack type, which appears to be characterised by a flat bottom, and no attempt at pressure design, at least as we understand it.  The lead top would be like a giant fusible plug.  Easy to be critical now, with our knowledge of the theory they still had to develop.  The truth is they did not know any better.

Hi Willy, I think Dan has answered the question about the haystack boiler design, but it was an interesting little diversion into history.  Obviously by the time your Lancaster design came along, they had a better idea of pressure vessel design, I can even see external reinforcing rings on those fire tubes.  They also clearly understood the importance of surface area for heat transfer to extract the maximum amount heat from the flue gas.  It will be great to see a test run on that one as well.

Very hard to put an accurate number on 'fair'.  The other problem is the table does not include values for thermal conductivity, specific heat and density.  I must admit to being surprised at the high temperatures suggested for TFE, perhaps of one of those things needing reliable citations.

Burning meths, or any other fuel for that matter, releases a fixed amount of energy per kg of fuel, based on its chemistry, and is not dependent on the initial air temperature.  However, that heat has to be absorbed by the combustion gases, which increases their temperature by an amount which depends on the density and specific heat.  If the air starts at a higher temperature, it reaches a higher temperature after combustion, from the same amount of energy released by the fuel.  The higher temperature of the combustion gases means more heat transferred to the water.  Hence the installation of air pre heaters on large boilers.  If the air is preheated using flue gas entering the stack, it reduces the fuel required, so increases the boiler efficiency.

For calibration of your thermocouple, it is important that you do not just use ice, but you need an ice-water mixture.  Ice and liquid water together behave much like liquid and vapour in equilibrium in that, at constant pressure, the temperature is constant.  At atmospheric pressure, the temperature for ice and liquid water together in equilibrium is zero deg C, and this is quite accurate enough to calibrate your thermometer.  If you can reduce the pressure enough, to just 0.6113 kPa, the triple point for water where solid, liquid and vapour all exist together in equilibrium is at 0.01 degrees C.  Ice can not exist in equilibrium above 0.01 C.  As the pressure is increased, water is one of those strange substances where it's freezing temperature gets lower, but as it is still only 0 at atmospheric pressure, you need a lot of pressure to get much measurable change. 

So ice and water together, well mixed until the temperature is uniform, when the ice starts melting, the temperature stays at 0 until all the ice is melted.  Of course it is a little tricky to get the temperature really uniform, a well insulated vessel helps.

Ice on its own can be much colder.  Just ask any of our members who live at high latitudes.  If you have ice at say -20 C, and gently warm it, it sublimes directly to vapour without ever melting to water.  So ice alone from your fridge, probably around -15 C for proper food preservation, is not a suitable reference.  You have to add some water and stir it until the ice starts melting and the temperature is constant.  A thermocouple probably only needs one reference temperature, though it is better to also check the readout instrument at a second temperature, and as I have mentioned before, the boiling point at atmospheric pressure is also suitable.  You do need to allow for the actual atmospheric pressure, 1000 hPa, 99.6 C, while 1013 hPa gives 100 C.  Again it is tricky to achieve a close to equilibrium temperature as you have to maintain the heat input to keep the liquid boiling.

I don't think that ice in a glacier is any different, though it has a lot of air mixed in when it starts as snow, then I guess the compression by more falling on top squeezes the water into the gaps and a lot of the air is lost, though some remains trapped for scientists in the future to measure the composition.

The next step in analysing my test run is to calculate the energy taken up by the boiler, specifically the copper and the water.  Now the copper is easy.  We assume the copper is the same temperature as the water, though in practice, is is a bit higher so that heat is transferred through the copper to the water.  The energy taken up by the water is in the steam tables as enthalpy of the saturated liquid, hf.  If we look up the hf for each recorded temperature, we can calculate the enthalpy difference.

My preferred method is to use a spreadsheet, as there is a lot of repetitious looking up the steam tables, and it all becomes quite difficult to check the calculations if done by hand.  However, spreadsheets have a function VLOOKUP, which is used to look up a value in a vertical column of a table or array of values.  So if I list all the temperatures I need, and use the steam tables to find hf for each temperature, the VLOOKUP function can be used to lookup the values of hf with a simple formula.

The attached picture is the top left corner of my spreadsheet.  You can see the table of enthalpy values in the first two columns.  It extends from cell A4 to B61, and if we make these absolute references by adding the $ signs ($A$4:$B$61), it can be referred to by a formula in a cell any where on the sheet.  It is relatively easy to recheck the numbers in this table, then it remains correct every time it is used. 

The next important columns you can see include the time and temperature recordings.  Then I used a formula to look up the enthalpy, hf for each temperature.  The formula looks like this:
=VLOOKUP(temperature, $A$4:$B$61, 2, exact match)

The '2' is the column of the table with the value we want for the temperature in column 1.  The 'exact match' is used to accept only that, most spreadsheets have an alternative term that allows the nearest match.  In this case it is better to get an error if the exact temperature is not listed, rather than just the nearest temperature listed. 

This might seem a lot of work, easier to look up a value in the book of steam tables, but then the magic begins.  If we copy that cell with the formula, then paste it right down the column, the computer looks up all the other values.  We can even copy the same formula and paste it to use it again for the cooling curves.

I have gone through that in tedious detail for those who may not have used that type of function before.  I hope it is helpful and encourages a few more to try.  And to expand the range of formulae you use in the spreadsheets you use.

I will continue with the energy analysis of the boiler test next time.

Thanks for following along,

MJM460