Talking Thermodynamics

[derekwarner]

Willy.....this may help. .....Imperial ,Si........any combination and in either direction.....Derek


http://www.tlv.com/global/TI/calculator/steam-table-temperature.html

[MJM460]

Engine Performance and testing -

Hi Paul, making measurements on your gauge 1 engines brings a whole new level of small scale to miniature instruments. If you have a suitable plug to replace with a thermowell, you could insert the thermocouple from a cheap multimeter into the thermowell to measure temperature while the engine was at rest.  Then just pull it out when you are ready to send the engine on its way.  Alternatively, you could hold the thermocouple tip against the boiler shell with an insulating pad of felt so it is not cooled by the air, and probably get close enough.  Experiments on a stationary boiler big enough to accommodate both would give you a good idea of the accuracy of this method.   I expect that you don't ride on the tender, so you don't really need to install the instrument on board.   The real size limitations are the batteries, unless you were prepared to use hearing aid batteries, and the screen, which clearly has to be large enough to be read.

Hi Willy, this link is to an open course on Thermodynamics and it includes a copy of the steam tables that can be downloaded as an Excel spreadsheet and read by most spreadsheet programs.
https://www.ohio.edu/mechanical/thermo/index.html
The course gets heavy quickly but you may find some interesting sections. 

The graphs don't use the volume of the water space, only the vapour space, and preferably the initial temperature.  Time is not relevant to the heat up graph, the non-linear part is just the water vapour pressure-temperature curve. 

Hi Derek, they tiv site is interesting, but I find a full set of tables is even more useful.  They hard to find on line though.    Hope you are now home safely from your travels.  The thread is getting close to your exhaust issue.

Willy recently asked if there was any point in an engine test on his horizontal engine.  I guess it applies equally to the Woolf Compound Mill engine.  So let's talk about what is required for an engine test, and what we can learn from a simple test.

Ideally for a complete engine test we need to measure the inlet pressure and temperature, the exhaust pressure, and if our boiler has a superheater, the exhaust pressure and temperature, more on that later.  We need to ensure the steam flow, and engine rpm, and finally we need to measure the engine output torque.  You see, we cannot predict the actual power that will be developed by a real engine, we do have to measure it.  This applies even to full size engines, though a full size engine manufacturer has access to many previous test results of similar engines, from which a pretty good estimate can be made for the engine efficiency.  However, if you as the customer want extra assurance that you will get the promised power from your new engine, you can specify, and pay for a full test on your engine after it is built.  Alternatively, you might accept the prediction and accept a lower cost simpler test just to prove that it runs ok without mechanical or steam flow problems, quite like our first runs on air.  With a known engine efficiency, or more specifically adiabatic efficiency, you can calculate the power which would be developed by an ideal engine, and from the efficiency, you can calculate the output of your real engine from the given steam conditions.

As model builders, we don't have access to many previous tests at all, let alone tests of similar engines to the one we are building, so we don't have a knowledge base of reliable efficiency data.  We are left with doing our own tests, so we need those instruments.  The temperatures are relatively easy, we have already discussed those, the more difficult ones are the engine inlet pressure, and the torque. 

Even that inlet pressure is easy if we are prepared to accept any pressure losses in our piping and regulator as part of the engine inefficiency, and we know the boiler pressure pretty well, at least if you have been following this thread.  But measuring torque requires more thought.  Most of the trouble with torque measurement is that our engines do not produce a uniform torque. For one cylinder, it goes from maximum to zero twice each revolution.  A two cylinder engine with cranks at 90 deg means four pulses per revolution, but at least the peaks are spaced so there are no zeros, but it fluctuates considerably nevertheless.  I know every dynamics text book describes a friction brake on the flywheel, and a good flywheel should keep the speed fluctuations to around 7%.  That should help, but I am not convinced.  I know I had to do a test with such a brake in my student days, and I really can't remember how much the reading fluctuated.  But we got pretty good at estimating the average or mid position of a vibrating needle, so that's what we had to do.  Now with electric integration and averaging it should be different, but there's no fun in that!  So I am thinking about a torque measurement which somehow averages the torque.  But, is there anything we can do without torque measurement?

I suggest that is a good place to stop and continue next time.

Thanks for looking in,

MJM460

[derekwarner]

I am sure there would be good fishing in the Ohio River where the cooling water from that  2.6M kW steam power station is located

Yes MJM...back in Wollongong however have not yet completed the exhaust temperature tests....[awaiting the insulation lagging to be completed over the new 1/4" OD exhaust line tubing]

Another question ...forward thinking...is 'to lag or not to lag' our gas tubing supply.......from the disposable canister to the refillable tank is fixed, however from the refillable tank to the burner jet is subject to considerable temperature change.....& occasional icing

I plan to install a gas isolation valve before the actual gas jet, then relocate the gas pressure gauge location to the discharge side of the  regulator. This way will then allow me to confirm the reduced gas pressure at the jet...........and also by isolating the boiler pilot pressure to the regulator, the actual gas tank pressure can be confirmed....

Derek 

[MJM460]

A simple engine test -

Good to have you back Derek.  I suspect they are not allowed to discharge cooling water into the river in Ohio, those very large concrete structures, the nearest one is issuing clouds of steam, I believe are natural draft cooling towers, and the white plume is the evaporating cooling water re-condensing in the cooler atmosphere.  A blow down flow is needed on a cooling water system, just like a continuously operating boiler and that is probably being treated and has time to cool in those low circular pools before discharge.  It looks like one tower is shut down, although there are designs which reheat the air above the coils to eliminate the plume.  I am not sure what the steam discharge from the stack is about, and that plume makes it hard to see the second stack, or precisely which is discharging that wisp of bluish smoke.  Perhaps some of our colleagues can come in with some more explanations. 

With your gas piping, remember the lpg in the container, whether the disposal or your refillable tank, boils just like water with latent heat and the two phase region, but at lower temperatures.  Your burner needs the gas phase, but the "l" in lpg is short for liquified.  The container has adequate mass in liquid form but  the liquid must evaporate into vapour for your burner.  As you don't have a heater on the container, the energy for the latent heat comes from the liquid, so it cools until heat in from the atmosphere is equal to that required for evaporation.  And at the lower temperature the vapour pressure is lower, so your burner sees ever lower pressure until the heat balance is achieved.  To get more heat in from the atmosphere, it is better not to insulate the pipe or even the bottle.  The ice on the outside of the pipe means the internal gas temperature is so low that the outside surface of the pipe is below zero, and moisture from humidity in the air first condenses then freezes on the pipe.  Removing that insulation will allow more heat in from the atmosphere, higher gas temperature, though it will still be cool, and most important, more pressure to the burner.  The regulator is probably running wide open, due to the low bottle pressure, so increasing the temperature in the bottle will help get your regulator back in control.

Back to those simple engine tests - You may remember I did a simple test on my mill engine some time ago.  Next job on the list is to repeat that a few times to ensure that I have consistent measurements.  I did measure the exhaust temperature, and came up with an efficiency for my engine.  Now I could do that test because my boiler, a fired boiler, though only Meths for fuel, has a superheater coil.  And it is quite effective.  With a boiler temperature of around 116 deg C, the superheater outlet was 138 C.  At that time, I showed the steam conditions on a temperature-entropy diagram and used the second law of thermodynamics to calculate the power output of an ideal adiabatic engine.  Yes that is repetition (tautology?), but deliberate for emphasis on the 'ideal' part of adiabatic.  I have repeated the diagram below for convenience.  The boiler outlet is point 2 and the superheater outlet is point 3.  The second law says the exhaust entropy of such an engine is equal to the inlet steam entropy, so the engine expansion shows as a vertical line on that diagram, the line from 3 to 5.  Entropy and pressure are enough to define all the exhaust steam properties.  You can see on the diagram, the adiabatic exhaust, point 5, will be only just wet steam, 99% dryness factor (by calculation).  Now my measured exhaust temperature was 104 C, meaning the real engine exhaust was superheated at atmospheric pressure, point 4 on the diagram where the remaining enthalpy is more than the enthalpy of saturated steam.  This basically means my engine had extracted less power from the steam than the ideal engine, and the ratio is the real adiabatic engine efficiency.  I don't have a torque measurement to calculate shaft power, but I know how much energy was extracted from the steam, before the inevitable friction losses and so on.

Now Willy's engine is in a different situation.  The engine itself is quite similar to mine to a casual observer, it is just better made.  But his boiler is electrically heated, and has no superheater.  In fact not easy way to add a superheater.  So the engine is receiving saturated steam, steam from point 2 on the diagram.  The ideal engine process is a vertical line down to exhaust pressure as before.  You can see from the earlier diagram that without the superheater, the exhaust steam is much more wet, or has a much lower dryness factor.  It looks quite likely that even a real engine exhaust would be in that wet, two phase region at atmospheric temperature.

Now the earlier diagram is not to scale.  It shows the two phase region as a bell shaped curve, very similar to any text book you care to pick up.  And gives the form of the curve in an easy to remember picture.  I did take care to ensure that point 5 is on the correct side of the saturated vapour line.  Also the constant pressure lines, 1-2-3 and the atmospheric pressure line through 5 and 4 are also the correct shape.  However, just to be sure that I am not being mislead by the out of scale part, I have re drawn the diagram to scale, and included it as the second attachment.  I am not the first to do this, in fact they are fairly easy to find as a complete T - S diagram for steam, covered with extra lines for every other property.  But the tiny part relevant to our model is so small it is difficult to pick up values with sufficient accuracy.  So the second  picture below is drawn to scale from the properties in the steam tables, and you can see that it is no fancy drafting job. 

We have talked about several operating pressures for Willy's boiler, I am still not sure if it was 143 or 148, and there was 135 and also 118 mentioned somewhere.  So I have plotted the constant temperature-pressure line for the boiler for 148, 135 and 116 so we can see the effect on engine performance over this range.  I have kept the temperature axis to scale to cover the exhaust at 100 deg C up to 150 C to cover over the 148.  I could not complete the bell curve on the paper at a reasonable scale, the top is at 374.14 C where the pressure is over 22,000 kPa, known as the critical point.  It is quite important in thermodynamics, so has been measured quite accurately.  Above this temperature or pressure, there is no distinct liquid phase.  But we don't need it for our calculations.  Similarly I have shown a second break in the curve which is bounded at the bottom by a straight line at zero degrees, where water freezes.  This does not have to be measured, it is a defined point on the temperature curve, as is 100 deg, the boiling point of water at 101.35 kPa and a few other points.  That is why we can use zero and 100 to check the accuracy of our temperature meters.

The enthalpy and entropy for dry saturated steam are both in the steam tables for 100 degrees, but the other temperatures needed some interpolation, a spreadsheet comes in handy for that.  Now using that second law condition, the adiabatic engine exhaust entropy is equal to the inlet entropy, I drew in the constant entropy lines which are vertical on this diagram, and calculated the dryness of the exhaust in each case.  You can see from the diagram they are very much to the dry end of the line, all above 90%, but it is better to do the calculations to get good figures for comparison.

That is enough to take in for one session, don't forget about the gas question either, so I will leave you with the diagrams to look at, and continue next time.

Thanks for following along,

MJM460

[steam guy willy]

Hi Mom thanks for this , I was thinking about making a superheater for this boiler but it would have to be an external one retrofitted and the electric control system would be necessary to avoid burning the element out.!! I was wondering how one might measure the exhaust pressure without restricting it as it just goes strait to atmosphere or is it calculated from the temp ?. I have just bought 2  (analogue) ? thermometers (griffen and george) and notice that the scales are different lengths so perhaps they are calibrated separately ? When using a superheater....the temp goes up and also the pressure ...,,but as it is an enclosed system is the pressure also in the boiler itself as well and how does this muddle the figures for the boiler temp/pressure etc ?? perhaps this is easily explained with the correct Maths ?!!! I may rig up the engine back to the boiler and it does have a small load on it withthw dynamo and the magnet driven cycle speedo, and perhaps this may be useful in any calculations......The magnet is placed in the periphery of the cast iron fly wheel. Looks like more fun on the way............The thermometers go up to 360 C but do they need insulating as they are about 12" long so doing superheating tests will be possible !!

[Gas_mantle]

Hi,

I've kind of followed this thread for a while now and learnt something along the way although I'd be the first to admit as a layman some of the technical info is way above my head but I'd like to ask a few questions of the experts.

As I understand it water expands 1600x when turning to steam at atmospheric pressure, if we assume atmospheric pressure is 15 psi am I right in saying that a boiler that can convert 1 cc of water to steam per min can theoretically run a 1 cc engine at 1600rpm using 15 psi (assuming we ignore heat loss, inefficiencies etc and the engine is single acting.)

If we take a small boiler like the GLR, how much water can something like that realistically convert to steam per min ?

[MJM460]

Superheaters and steam volumes -

Hi Willy, your superheater design concept is spot on.  It might be well worth making that central sheath for the element hollow right through and soldered into both ends so you can put the element in, with some heat transfer grease and put a thermocouple in from the other end for your over temperature protection.

 However a few points to be aware of.  Heat transfer is not nearly as good to steam as it is to boiling water.  To put numbers on it, my heat transfer text book gives figures of 30 - 300 kJ/ m^2.K for superheated steam, and 3000 to 60000 for boiling water.  The wide range in each case makes them difficult to use in design, but you can see the difference in magnitude.  So heat transfer is limited by the steam side film coefficient.  You need lots of area and this is where fins come in.  The higher the fins the better, within reason.  Of course flow is longitudinal, so you need longitudinal fins.  Plenty of build logs present ideas on how to machine these.  You also need a lower heat intensity element, that is more surface area per watt of rating.

 It is not all bad though.  If we look at say 400 kPa absolute, 143.6 deg C, a touch over 40 psig, the enthalpy of the dry steam leaving the boiler is 2738.6, while superheated steam at the same pressure and say 200 deg C enthalpy is 2860.5 kJ/kg.  Only an extra 122 kJ/kg compared with the 2133.8 kJ/kg which the boiler needed to evaporate the water at 143 deg C to dry steam at the same temperature.  You can see that the superheater element only needs to be 50 or 60 watts to nicely compliment your boiler and achieve plenty of superheat.  But it will be harder to transfer that heat to the steam, and the element will tend to run hotter.  So a low intensity element, access for heat transfer grease and a thermocouple for your temperature protection, longitudinal fins as high as possible, and plenty of insulation.  You will need a condensate drain to aid startup which will require a bit of thought so as not to overheat anything.

Those thermometers may be individually properly calibrated for a small variation in the diameter of the capillary that carries the Mercury column up to the appropriate scale mark.  I don't know much about the manufacturing process.  I believe there is an error in the readings due to heat transfer along the glass, and it can be calculated, but it's lost in the ancient mists of school science.  Alternatively it might be possible to reduce it to an acceptable level by insulating the part of the stem below your expected reading with some felt or silicone tubing.

In the superheater, the pressure does not increase.  If anything, there is a small pressure loss due to pipe friction as the steam flows along.  Assume boiler pressure and use a generous size tube between the boiler and superheater.  That line 1-2-3 on the first diagram yesterday is a constant pressure line, the pressure is no longer a straight horizontal line outside the two phase region. 

Using a bike speedo for rpm should be ok so long as you use the wheel size set in the device to calculate rpm from the wheel circumference and speed.  The Dynamo will provide a nice little load.  Unfortunately the V and I measurements do not give us engine power as we do not know the electrical efficiency of the Dynamo.  That is why we need torque measurement.  But V x I does give a sensitive indication of load changes.  Just be aware that efficiency might also be changing.  We should be able to see a slower run speed, higher steady boiler pressure and lower steam rate with the load on, to compare with the free running unloaded engine.  We should then be able to see and  compare the power output of our adiabatic engine which will be an indicator of the actual load.  The exhaust will most likely still be in the wet region so temperature measurement is not useful.  But it  should be a worthwhile run in every way.

Hi Gas Mantle, great to have you on board.  The purpose of this thread is to try and make that technical information understood and accessible to all, so all questions welcome.  The expansion as steam changes from liquid to vapour is best found by using the specific two volume columns in the steam tables.  The precise figure for standard atmosphere is 1602 times.  At 15 psig, say 30 psi absolute, or 206.8 kPa.  Compared with the steam at atmospheric pressure the steam at 15 psig is compressed and so a smaller volume.  I will round that pressure out to 200 kPa (if you look at the tables you will see why), and see that the specific volume of the liquid vf, is 0.001061 m^3/kg, while the specific volume of the dry saturated steam, vg, is 0.8857 m^3/kg.  A simple division, using a calculator gives an expansion ratio for 15 psig of 835.  So a perfect 1cc single acting engine should run 835 revs for each cc of water evaporated at 200 kPa.  Or 1 cc per minute evaporated should give 835 rpm.  I have found it hard to match the figures in practice.  Valve leakage, piston leakage and any valve overlap all increase the steam consumption, or reduce revs, while early cut off should decrease steam consumption.  I am still working on just which it is, or possible all the above on my engines.  But it is a valid starting point. 

The fundamental limit to how much steam a boiler can raise is the amount of energy in the fuel you  burn.  Weigh your fuel container (with burner attached is ok) on the most accurate digital scale you have access to, before and after a timed run and calculate the mass of fuel burned.  Doesn't matter that boiler first heats up, then generates steam, as the burner fuel consumption should be pretty constant with time what ever.  Then look up the fuel calorific value, I can probably find a figure if you tell me what fuel you use, and multiply the two to get the energy from the fuel.  Then it depends on the boiler how much of this is turned to steam.  The gas from the stack is hot, so that tells you that energy is being lost, and it can only be cooled to a temperature something above the steam temperature in the very best boilers, so some loss from that source is inevitable.  There is also radiation from the boiler casing.  So the next experiment is to see how much steam you are getting. 

You will have seen from the calculations on Willy's boiler that it is helpful if you can weigh the bare, empty boiler, otherwise calculate it from the density of copper and the boiler dimensions and thickness.  Weigh a suitable amount of water into the boiler, light up and run for a suitable time, and carefully time from light up to first steam, and on to flame out.  Finally carefully drain and collect all the remaining water from the boiler.  The water evaporated is obtained by subtraction, and the time for that evaporation is from the first steam to the end. 

So you can now work out how much heat to raise steam, and how much heat was used to raise a known quantity of steam.  From that you have your boiler efficiency, which you can use with reasonable confidence for future runs of that boiler.  If the boiler has too little heat transfer area, the stack gases will be hotter and more heat lost.  If it has plenty of area, the stack gas will not be as hot, and if necessary you can give the burner more pressure or use a larger burner.  I don't know the particular boiler you mentioned, but testing the burner and calculating the heat transfer area will give you a good idea of how it would perform compared with other similar boilers.  I hope that helps, but don't hesitate to ask for any clarification you require.  Others will probably be wondering the same thing.

I think that is enough for a session, so I will try and return to those t-s diagrams and what we can learn from them next time.

Thanks for reading,

MJM460

[Gas_mantle]

Thanks 

I seem to remember reading somewhere that small copper boilers like the sort of thing hobby engineers use should be able to evaporate 1cu" of water per min for every 400sq" of surface area in contact will the water.

Does that sound about right as a very rough guide? I can't remember where I read it and may have got the figures wrong.

[paul gough]

Re lagging and heat losses. Reading in, 'The Efficient Use of Steam', by Oliver Lyle, 1948, the author concludes for steel pipes 3" dia or below with internal temps. of 300 degrees F., (which would work out for us at about 50 p.s.i.g.), a lagging thickness, (85% magnesia or asbestos), of 1" is sufficient, his chart shows approx. lagging surface temp. of 107 F. in still air 70 F. A lot of our model boilers are made of copper so I assume heat loss potential higher than a steel pipe. Author quotes heat loss for a bare 6" steel pipe in still air with internal temp. of 300 F. as 646 Btu/sq. ft./hr. and 98 Btu loss for 1" thick lagging. A common dia. for 5" and 71/4 gauge locos.

Question; (1) Are the insulating properties of our much used Kaowool sheet insulation comparable to the above materials?

               (2) 1" thick insulation on a 3" boiler is pretty thick by most builders standards. Are we underestimating the thickness we should
                     apply to our boilers when there is room to do so?
                                                                                            Regards, Paul Gough.

[steam guy willy]

Hi MJM ,thanks for the suggestions about the superheater design. I was going to use a 500 Watt element i have in stock but if i did use this what would happen ? in a Locomotive the superheater goes back into the firebox where the fire is at its hottest !! so do we not need to do this ?

[MJM460]

Boiler potential, insulation and superheater design -

Hi Gas Mantle, that rule of thumb for boiler capacity has a very similar form to that in the K. N. Harris book on boilers.  It is not without basis, but has some big implied assumptions that really need to be stated whenever it is quoted.  Dan was asking about it some time ago and I have been waiting for an opportunity to get back to it.  For a start, look at the dimensions of the terms.  A valid equation has first to have equal dimensions on each side of the = sign.  You cannot add or multiply apples and oranges.  So that constant, 400, has dimensions to make that side of the equation dimensionally the same as the other side.  Undesirable, but no real problem, it just means that the correct units must be used, cu.in/min on one side and square inches on the other side, or a bit of work to calculate the equivalent constant for use in other systems.

   If we go back to the basic heat transfer equation (it was discussed back with condensing,) Q=U x A x delta T.  The simple form does hide some complexity.  First Q has units of Watts, but so long as consistent units are used both sides, you can equally well use Btu/hr of you prefer, and you use consistent units for the other quantities.  The delta T is log mean temperature difference, and should strictly be written delta T lm with the lm as subscripts meaning "log mean to base e".  For SI, the units are deg C, and it is a temperature difference so you can use C or K (or F or R).  A is straightforward, m^2 for SI, (or ft^2).  U is more complex, but it's units are W/m^2.hr.C, (Btu/ft^2.hr.F) and unfortunately it is not a simple constant, nor is it easy to predict a value.  Whole books on that subject are heavier in every way than thermodynamics books.  They get there in the end, but I don't intend to go there. 

If we compare the two formulae, we can see the similarities.  A cubic inch of water has a fixed mass, particularly of the temperature is specified, and that mass takes a known amount of energy to evaporate it, again "known" means using the steam tables and requires the pressure or temperature to be known.  So cubic inches can be regarded as a proxy for heat input to the water.  Now in most model boilers, neither the delta T, nor the heat transfer coefficient is known, so it is not unreasonable to combine the two into one factor.  But you can't easily determine what this factor will be.  For example, for a coal fired locomotive the temperature in the firebox will be pretty high.  A very different temperature would apply for a gas burner, or a methylated spirits burner, so any figure determined by a boiler test would really only apply to the same method of firing.  Then the log mean temperature difference, LMTD, varies with the arrangement of area and gas flow through the boiler, so would strictly only apply to similar boilers.   But more than that, both the LMTD and the maximum possible heat transfer are limited by the burner size.  Conservation of energy is a fundamental law of physics and it means in this case you cannot transfer more heat into the water than is released in the firebox.  Basically if you have a small fire in a big boiler, the stack gases will be cool to only a tiny bit above the steam temperature quite quickly, and the rest of the boiler area just gets a tiny bit closer.  On the other hand, if you put a huge burner into a small boiler, you will definitely get more steam than from the small burner, but the flue gases will arrive at the stack before they have lost all the heat that can be transferred at the steam temperature if the area was bigger, and so will go up the stack at higher temperature, wasting some the energy in the fuel.  You can see the problems, however, I would guess that formula may have been arrived at based on coal fired locomotive boilers.  Similar successful boilers might well be consistent enough in proportions of fire box and heat transfer area to come close to following this simple formula.  I don't have a better idea, so as long as the formula is used as a rule of thumb, with understanding of its limitations, it can serve as a starting point for design.  It could be useful for scaling up an existing boiler which you could test, to a larger scale similar boiler with a similar arrangement.  If you were starting a new locomotive design, you could run a few calculations in a spreadsheet for some of the past entries in the various locomotive efficiency competitions, to get an idea of the applicability of the formula.  Then add data from any tests you are able to do on your own models.

Hi Paul, generally industry places a high value on the immediate cost of materials and labour costs to apply insulation, and undervalues the long term cost of the energy losses which are usually incurred "by others", so insulation thicknesses are generally less than desirable for heat conservation.  You can also see it in domestic fridges, where the sales hype is the illogical assertion of more internal volume for storage of your food within the smallest possible outside dimensions.  The salesman does not place any value of the insulation hidden between the outside shell and the liner.  And the average plastic Esky has no insulation in the roughly 1/2 inch gap between the outside shell and liner.  And simply, yes, we put too little insulation on our models for heat conservation purposes.  But note that qualification, in our models we are trying to optimise size of the boiler, heat transfer area and appearance, and the fuel cost is not high for the typical number of operating hours, while appearance is paramount.  So we have valid reasons for using minimal thickness.  It is usually simpler to achieve performance by pouring in more heat.  But whenever we can apply some insulation, it reduces heat up times and gives more steam for a given fuel burning rate, and reduces the incidence of burnt fingers, and if it is practical, more is better.

K values for some suitable insulating materials in Watts/m.K - cork 0.04, glass fibre 0.035, kapok 0.035, plaster 0.814, polystyrene 0.157, softwoods 0.15, oak 0.19, wool 0.038.  I also have 50% magnesia 2.68.  Asbestos is 0.113, so not only dangerous, but not the best for insulation value.  It was used because it has fire resistance at really high temperatures.  All compared with copper 83 and steel 43.  Steel will have a higher temperature gradient than copper, but with insulation restricting the heat flow, both temperature gradients will be small enough to be insignificant.

OK, Willy, what will happen when you use a 1000 watt element in your superheater?  It's easy to apply a few numbers and this will require us to look at the superheat section of the steam tables. This section looks complex, but it is actually a quite simple separate table for each pressure.  Each little table starts at the saturation temperature, steam is not superheated below that, then jumps into a sensible series and has a single column for each of specific volume, internal energy, enthalpy and entropy.  So let's look at the steam from your boiler at 400 kPa abs, about 42 psig, that we used last time as the superheater input.  You will remember the enthalpy of that dry saturated steam leaving the boiler was 2738.6 KJ/kg.  And if you look back at the saturated steam section of the tables, you will see that your 1000 Watt element put 2133 KJ/kg into each kg of steam to evaporate it from water at that temperature.  Now remember your electric heater delivers its rated power output by increasing its own temperature until the heat transfer is enough.  In your superheater, your 1000 watt element will just get hotter until there is 1000 watts of heat transferred.  So you will add 2133 kJ/kg to the steam from your boiler.  The superheater outlet enthalpy will be 2738.6 + 2133 = 4871 kJ/kg.  Now we look up that enthalpy in the little superheat table for 400 kPa, and it is there.  (You can see that enthalpy is turning out to be a very useful concept).  Look across to the temperature column (it's on the left side of the page, but applies right across that line on the page).  Superheated steam with an enthalpy of 4871 KJ/kg has a temperature in the range of 1000 to 1100 deg C, you need to interpolate to get a precise figure.  I am assuming the heat loss is no greater than that from the boiler, so I assume some good insulation.  So what would that temperature mean?  Well the code design for copper boilers generally does not give a strength for temperatures above 200 or 250 deg C, so your boiler inspector would probably require a steel boiler, among other things if he knew the predicted discharge temperature.  Yes, the superheater is classed as a pressure vessel and requires testing and approval.  (Strictly, piping also).  If the copper temperature goes above 200, the strength continues to reduce, until copper melts at about 1350 deg C, so I would expect it to be pretty soft at over 1000 C and the shell would probably bulge at some point.  Not like a balloon, but a sizeable bulge, then as the boiler continues to maintain the pressure, it would split!  However silver solder melts at a somewhat lower temperature, so the ends or bushings might blow out first.  Of course the heater element has to be a bit above the steam temperature, so it might burn out before we get to this temperature.  It's a bit of a race to see which fails first.  But there are no winners in that race, whichever outcome, it will end in tears.  Better hope it's the element, 'cos steam that hot steam is very dangerous.  Just as well this is a hypothetical experiment, it's not a wise one to carry out with real equipment, however small.  Better stick with the recommendation last time of 50 to 60 watts, then the outlet temperature will only get to about 200 deg, so long as you maintain the steam flow.  I hope that makes the design process a bit clearer.  So you still need a high temperature cutout, and it should operate if there is high temperature or if the boiler power is cut.  That is an inclusive OR, either one or both should cut the superheater power.

Of course you may ask about using a controller to reduce the operating time of the heater.  It's possible with PWM of the power supply or other fancy digital controls.   The issues are reliability and heat transfer element intensity.  It is very hard to adequately cool the element when your fluid is dry steam instead of boiling water.   And all the while, you are a single failure of one of the internal electronic components away from 1000 degrees.  This is not intended to be a damper on the idea.  It is quite practical to build an electrically heated superheater as you suggest, they are used in industry.  You just have to understand the heat transfer and thermodynamics to develop a safe and realistic design.  If the elements of the lower rating are not available you could use say 100 Watt with a controller, or a transformer to reduce the voltage.

The last point, you are correct in that if the heating was from say a heat transfer oil which changes temperature as it looses heat, you would arrange the flows to be countercurrent, however the element is nominally a constant temperature device.  Think one of those one bar electric radiators, it's the same temperature all the way along as the heat is produced evenly in each metre of wire.  In the superheater, the steam temperature rises as the steam flows along the element, so the element temperature has to change in response to maintain the heat transfer all the way along.  If you connect to the other end, the hotter end of the element will always the outlet end.

I hope you find that interesting and helpful in you consideration of an electric superheater.

Thanks to everyone for looking in,

MJM460

[MJM460]

Back to Adiabatic engine discussion -

Those little diversions have given us an extra interesting steam condition to add to our exploration of the performance of an adiabatic engine.  You might remember that a few posts back, (post #363)
that I drew the relevant part of the T - S diagram to scale and showed three of the boiler temperatures we had been looking at for Willy's boiler.  (The second diagram)  The horizontal lines labelled 118, 135 and 143 (all deg C), show the boiler process for evaporation of water at those temperatures, while the one labelled 100 (deg C) is the condensing process for steam at standard atmospheric pressure.  The one labelled 15 shows condensation (or boiling) at the atmospheric temperature of 15 deg C.

There is a table to the right of the diagram which shows the saturation pressure in kPa (abs) for those temperatures and the entropy at the wet and dry ends of the lines, sf and sg.

 If we supply steam at one of those conditions to an adiabatic engine, then the second law of thermodynamics says that for this ideal engine, the exhaust entropy will be equal to the inlet entropy.  (Any real engine exhaust will have higher entropy.)

This means that the ideal engine expansion is that vertical line from the dry saturated steam leaving the boiler to the exhaust steam line.  The lines for the three conditions are very close together, so I have only drawn two.  You can see they all arrive at a wet steam condition.  In the wet steam or two phase area, temperature and pressure are not independent, but we now have the entropy at the exhaust condition, and this is enough to completely define the steam properties.  You see even entropy eventually comes in useful.  It is a property of the diagram that in the wet steam, the mass fractions of liquid and vapour are proportional to the values between the liquid and vapour lines for example, sf and sg, and as we now know those values, that fraction can be calculated.  Then the same fraction applies to all other properties, in particular, enthalpy.  So we can now calculate the enthalpy at the exhaust steam condition.

I have calculated those values and summarised the results in the table at the bottom of the diagram.  And the last column is the difference in the engine steam inlet enthalpy and the exhaust enthalpy, which is the work extracted from the steam by the adiabatic engine.   These are all on a per kg basis, but if you multiply by the steam rate, you have the ideal engine power output.    Remember, these are for an ideal engine, and the output of any real engine will be much less, but they are a maximum limit, and show the difference in potential output for different steam conditions.  You can see that the answer from subtracting two large quantities, the enthalpy of the supply steam and enthalpy of the exhaust steam which are a similar magnitude, is only about 10 % of either of those quantities, so it is necessary to try and carry the calculations through with the same accuracy as the tables to minimise the accumulation of errors.

You can see that as you would expect that the engine provides more output from the higher pressure steam, but you might be surprised at how much more compared with the extra heat input to the steam.  For example the ideal engine output is nearly doubled between 118 and 135 deg C inlet temperatures for about 1% extra energy input.  You can see why industry aims for ever higher temperatures and pressures.  I'm not suggesting that the model engine output is doubled by this higher inlet temperature, but there is no doubt that the potential power output is significantly increased.

It is also interesting to note that at higher temperatures, higher up that bell curve, the energy output to evaporate the steam, hfg, reduces, the increased energy contained in the higher pressure steam is all put in during the boiler heat up phase of our simple boiler, and once up to temperature the boiler can produce a small amount more steam, perhaps further increasing the engine output for our burner capacity.   Of course with continuous feedwater injection, the heat up and evaporation process happen at the same time, so for a given burner or electric element size, there is overall less steam produced.  Might be worth fiddling a bit more with the calculations to try and extract more understanding.

Now Willy has proposed a superheater.  To save a little effort in interpolation, I worked the example  at 143 deg C where the boiler pressure would be 400 kPa.  A pity it is not on the diagram, but the lines were getting to close together.  However a close look at the figures on the diagram suggests the 400 kPa steam inlet, would give exhaust steam about 0.925 dryness fraction and an engine output around 220.

When we add the superheater, the 50 watt one of course, to give 200 degrees C the steam enthalpy is 2860.5, and the entropy, from the superheat table, is 7.1706, compared with the 6.8959* (*note this figure has been corrected after the original post) of saturated steam, but still less than saturated steam at the exhaust temperature of 100 (7.3594). From this we can calculate exhaust dryness = (7.1706-1.3026)/(7.3594-1.3026) = 0.9688, clearly much more dry with the superheater, but still in the wet region.  We can then use this figure to calculate the exhaust enthalpy = 0.9688 x (2675.5-417.46)+417.46 = 2605

Finally steam inlet enthalpy - exhaust enthalpy = 2860.0 - 2605 = 255.5 KJ/kg.  This is a lot more than from the saturated steam but only little higher than if the boiler was operated at 148 deg,  possibly not enough to be worth while.  Perhaps we should make the superheater a little bigger to give say 250 deg C.  This would give us dry steam exhaust but more importantly  would show a real benefit  for the superheater compared with the boiler a little higher pressure.  I repeated the calculations for 250 deg C superheater outlet temperature, it requires 105 watt element, and increases the adiabatic engine output to 280 KJ/kg.  This looks like it would be more worthwhile.  The adiabatic engine exhaust would be very close to 104 deg C.  But worth looking at the boiler temperature required to achieve this output without superheat.

By the way, if a 100 - 110 W element is not available, remember the power is proportional to V^2.  So if you use a 240 - 110 V step down transformer, a 500 watt element rated at 240 V will produce about 105 watts at 110 V.

Another interesting point is that the specific volume of the superheated steam is higher, the superheater increases the volume of the steam.  If the engine can't run faster to use the extra volume, the system pressure right back to the boiler will rise unless the heat input is cut back.  So for a free running engine, whether loaded or not there will be a new balance of steam pressure and flow to use all the energy put in.  Remember the superheater cannot produce more pressure than the boiler.

You can see there is value in doing some calculations before you start cutting metal in order to reduce the amount of error in trial and error.  We still have to look at what all this means for a real engine.

Thanks for stopping by,

MJM460

[Gas_mantle]

Thanks MJM,

As a general principle do small model boilers generate more steam when coal fired as opposed to gas ?

[steam guy willy]

Hi MJM thanks for this new info.....I did hesitate when trying to make a superheater  as i thought there might be problems with this design !! I was wondering if the superheater pipe was inside  the boiler heater sheath would this work ,a bit like a locomotive superheater that is actually in the fire box.As this sheath is at the same temp as the water it is boiling it is not at a much higher temp??

[MJM460]

Superheaters and real engines -

Hi Gas Mantle, I don't have direct experience with coal fired models, but I am sure there are many others on this forum who will be able to answer your question.  However a few observations can be made that might be relevant to understanding the issues.  First, with coal, you need a critical mass of hot coals to sustain combustion, just putting a match to coal will burn a little coal while it is there, but the fire does not continue when the match is removed.  You need a bit more concentrated heat  to make a coal fire which is self sustaining.  In addition you need an adequate draft to draw enough the air through the coal bed, and of course space for a big mass of coal and lots of draft are both in short supply in a small model.  You can do quite a bit with the coal particle size, but I suspect there is a minimum practical size for a coal fire, and I don't know how much coal the smallest practical fire could burn in a given time, or at what rate coal could be burned in a small model.  With gas, the particle size is molecular, and so long as you have a steady supply and the appropriate air/fuel ratio, the tiniest flame will continue.  At the other end of the scale, even in a small model, the available gas pressure means you can burn a relatively large mass of fuel with ease, and the gas pressure provides energy to achieve the required draft.   On the other hand, a coal fire has a very high transfer rate for radiation heat transfer.  The predominance of energy in that red and infra red region gives very high radiation coefficients.  The energy distribution in a clean gas flame is biased more towards the blue and beyond, which results in a lower radiant transfer coefficient.  You can feel this difference by holding your hand an appropriate distance from the flame.  So a coal fire can transfer much of its heat by radiation, where the high temperature helps more, leaving less to transfer by convection.  A gas fire does not transfer as much by radiation, so generally needs more area for convection heat transfer.  Some people insert a wire coil in the gas path to collect heat by convection from the hot flame.  The wire in turn glows red, and radiates more efficiently to the tube surface.  I don't know how well this works in practice, but it has a sound basis.

So the question is more complex than it might seem, and the answer really relies on experiment.  The theory should help understanding of the experimental results, but ultimately you need to talk with people who have done the experiments.  If you have a suitable small boiler, experimenting with each fuel, including coal size, bed depth, blower arrangements and different gas burners to see which will evaporate the most water in comparable arrangement would be the best way.  I seem to remember that Florian's Cochrane boiler is set up to allow both fuels, but it is probably not a small as you are thinking.  Comparison between different boiler arrangements is more difficult.  If the fuel rate releases the same amount of energy for two cases, they should be able to produce the same amount of steam, but coal will probably give better results with a generous firebox for radiation transfer, while gas will probably need more area in the flues for convection.  I will be interested to find out what you are able to learn.

Hi Willy, I am having trouble imagining how you would put the superheater tube in the sheath with your electric element.  Remember, you element just gets as hot as it needs to in order to loose all the heat generated, and relies on good cooling of the sheath to limit the temperature rise so the element does not melt before it rejects enough heat.  For a boiler, you slide the sheath into a close fitting tube which is part of the pressure containment, preferably with some heat transfer grease to aid transfer to keep the element cool.  You can't make it loose enough to accommodate a superheater tube, as the element cooling would not be adequate in a sheath with enough excess space.  I suppose you could use a solid rod of brass or copper, and drill two or even three holes length wise, one a close fit on your element and the other one or two fitted at each end to connect to the steam pipe.  I am not sure if you would get a high enough temperature in the steam tube to be worthwhile.  Heat only flows from hot to cold, and you need enough temperature gradient to transfer enough heat.  Remember the example with superheat to only 200 degrees compared with a higher boiler pressure.  It would be difficult to control the heat distribution to achieve adequate superheating, and at the same time adequately cool the heating element.  Your separate device concept is not only easier to analyse, it is more flexible in operating conditions, and I suspect it would be much more successful.  But an interesting idea to ponder if the specification sheet for the element allows a high enough temperature.

In a fired boiler, you are correct that the conductivity of copper means the copper is quite close to the water temperature, but still higher, as heat is transferring from copper to the water, but the flue gas is at much higher temperature to transfer all this heat via convection to the copper.  I suspect though that while the superheater tube passes through the flue tube, most superheating might occur in the part exposed to radiant heat in the firebox.  This could also be why many writers question the effectiveness of these superheaters.  You can see the arrangement is quite different from the one in my small boiler, where the steam tube is run into the fire box, two turns around the firebox, then straight out through the furnace wall from where it is insulated until it gets to the lubricator and engine inlet.

Last time, I looked at the performance of an adiabatic engine based on a few steam temperatures from Willy's boiler test, and I suspect typical of what many of us achieve.  The exhaust steam was generally in the wet region, however even the wettest exhaust steam was over 90% dry steam.  So, even in an ideal engine less than 10% of the steam arrives in the exhaust as liquid.  I don't think this is enough to explain the troubles Derek is having with condensate, but let's look at a what happens in a real engine.

Unfortunately, after being so useful in our consideration of the adiabatic engine, the second law of thermodynamics goes all wishy-washy for a real engine.  It just says the entropy of the exhaust will be greater than the entropy of the inlet steam.  No clue at all about how much more.  This means we do not know enough about the exhaust steam to do the calculations we did for the adiabatic engine.  Following on from the lack of information about entropy, the implication of exhaust entropy being higher for a real engine than an adiabatic one is that the exhaust enthalpy of a real engine will be higher than for the ideal engine, meaning that less enthalpy is converted to work in the real engine, but we don't know how much less.     In fact, it is necessary to do an engine test in order to find out how much power any real engine develops.

The simple engine test I did on my engine gave an exhaust temperature of 104 deg C.  Now this is above the saturation temperature for atmospheric exhaust pressure which means the exhaust is superheated.  Only just, but we would not expect any condensate in the engine.  Now the constant pressure line in the superheated steam region is no longer a constant temperature, and the temperature and pressure are now enough with a little interpolation to determine all the properties of steam including the enthalpy, so we can calculate the work extracted from the steam.  When the calculations are carried out, my engine extracted about 66% of the enthalpy extracted by the ideal engine.  This figure is defined as the adiabatic efficiency of the engine, and you can see why an engine manufacturer might prefer to quote this instead of the thermal efficiency.  But at least it tends to be independent of the steam conditions over a reasonable range, so there is some justification.

You will have noticed that I have been very careful not to call the work extracted from the steam the engine output.  We would hope that it is indicative of the shaft power output, but it is worth looking in a bit more detail at just what this figure represents.  A great topic for another time, but there is a little more to learn about exhaust steam first.

Thanks for looking in,

MJM460