Talking Thermodynamics

[steam guy willy]

Hi just wondering about waste heat and thermocouples ?? at least it should power a transistor radio for the fireman to listen to the latest action from Headingly, !!! is there any info about this anywhere ? It could even illuminate pressure gauges and things on dark nights on locomotives !! I can remember in the Practical Wireless Mag from the fifties a design of a thermocouple connected to a Hooka for people to listen to the radio in India,!!

[paul gough]

Thanks for your comments MJM. Funny you should mention utilising a stationary engine for test purpose as only last week when discussing my 'headaches' with another I mentioned how I might be driven to getting a twin horizontal stationary engine so as to test two alternative materials at the same time and measure their relative performance.. This little project is likely to run into years, as there are other challenging things that please me to tackle. 'Adequate' lubrication rather than the general flood of oil that is often a messy characteristic of these little engines  and multiple orifice blast nozzle so as to eliminate back pressure, just to mention two. One of my 'madnesses' is to develop a mechanical lubricator for Gauge One size locos. Desktop size engineering is somewhat challenging and should keep my old brain from rusting up even if the body fails and manufacturing things becomes beyond me.

 Your exploration of things theoretical presents aspects for consideration that are often unknown or overlooked and I am very pleased to be able to read your words and also the responses and questions they provoke. This thread is a unique opportunity to begin to understand what is happening  and progress the ideas of miniature mechanicians. Thank you. Regards Paul Gough.

[MJM460]

A theoretical limit-

Hi Willy, that is a good idea.  It is called the Peltier, or Seebeck effect.  Both are reversible in the sense that if you pass a current through a pair of junctions in one direction, one gets warmer and the other cooler.  Reverse the current and the hot and cold sides are reversed.  Reverse the heat flow, supply the heat instead of electrical energy, and you get a current.  Small units are readily available as drink coolers/heaters in camping and car accessory shops.  Discreet units are sometimes available in electronics outlets, and certainly on line which can be heated to get a current.  They are not very efficient but we will come back to that.  Thermocouples only give about 5 mV for 100 deg C temperature difference, or is it microvolt?  Either way you need a lot of junctions.  But some combinations of semiconductors also work, and much more efficiently.  I found a reference which implied about 6% energy conversion to electricity.  Does not sound impressive, but if 70% of our burner energy goes to the condenser, and we convert 6% of that to electricity, that makes 4.2% of the fuel turned to electricity.  For a small model that is much more than the engine output, so more than doubles the output of our plant.  Worth a few experiments perhaps.  Of course we do have to carry the heat away from the cool plate, or it soon approaches the exhaust temperature and electricity stops.  Still need a river or a cooling tower, or perhaps a good heat sink and use some of the power to drive a fan so air carries away the heat.  Try looking for Peltier or Seebeck, or Peltier-Seebeck effect in your preferred search engine.  Similarly if you have one of those three way camping fridges which have a low power absorption refrigeration cycle, it may be possible to replace the heating element with your exhaust steam as a heat source, and keep the beer cool.  Not sure if it could be scaled up to full size plant.  In industry, refrigeration plants using absorption cycle are sometimes used when there is a large source of low grade heat together with the need for refrigeration.  But to be economical, they are normally huge.

Hi Paul, thank you for your kind words of encouragement they are much appreciated, as are all the questions which keep the thread rolling along.

My thinking on a small test engine was to avoid the work and inevitable damage involved in disassembling a locomotive to do many tests.  I thought a single cylinder mill engine style would enable easy manufacture and installation of the relevant test components, so speed up the learning process.  The valve gear can be a simple eccentric for piston ring and piston valve tests, or as complex as you like to test valve gear variations.  It is a test instrument, not a historical model, so optimise it for easy changing of components.

Engineers wanting to sell their engines were not really impressed with low efficiency, and wanted to claim higher figures.  Sadie Carnot was looking at how high the efficiency of an engine could be.  I think it had previously been concluded that 100% was not possible, it was determined by the maximum and minimum temperature of the cycle, but what was possible?  He came up with a theoretical ideal (even though not very practical) cycle which he was able to show would have the maximum possible efficiency, which he showed could be calculated as 1 - Tl/Th.  This is a fraction which can be multiplied by 100 to give a percentage.  The temperatures are expressed in absolute terms so K or R , depending on your preference.  Tl is the low temperature at which heat is rejected, or condenser temperature.  Th is the maximum temperature at which heat is supplied, the boiler pressure for saturated steam, or the superheater outlet temperature. 

We could calculate the efficiency of a Carnot cycle engine operating between our cycle temperature limits.  That 4 MPa boiler we looked at earlier, had a superheater outlet temperature of   400 C or 673 K.  The condenser temperature for 10 kPa would be 46 C or 319 K.

We can calculate the efficiency of a Carnot cycle between these temperatures as 1 - 319/673 =  0.53 or 53%.  Now remember the thermal efficiency of the actual cycle was 35%, If 53% is the thermodynamic limit of what can be achieved, we can perhaps say our cycle has 35/53 = 66% of the Carnot efficiency.  Sounds a lot better than 35%, doesn't it?  We could do a similar calculation for our model.  But it also raises the question, why not build our plant to operate on the Carnot cycle?

I will try and look at that next time

Thanks for your interest and encouragement

MJM460

[MJM460]

After yesterday's post, I must apologise to M. Carnot for spelling his name wrongly.  Nicholas Leonard Sadi Carnot lived from 1796 to 1832, and published his work around 1824.  A salient reminder of how our life expectancy has changed since then.  If a Carnot cycle engine has the highest possible efficiency for an engine working between specified temperature limits, why not make an engine working on the Carnot cycle?  The truth is that it is not a very practical cycle.  It produces very little work and it would be difficult to make one that would overcome its own friction even.  It's only real use is to quantify the maximum possible work that can be obtained from a given temperature difference against which you can compare the performance of a real engine.  But all is not totally lost, there is actually one real engine that has the same maximum efficiency as a Carnot engine working between the same temperatures.  It is the Stirling cycle, which many forum members enjoy.  It has disadvantages in terms of power for its size unless you have a pressurised engine with sophisticated seals, but it is inherently a very efficient cycle, especially if the the regenerator is included.  It's efficiency is illustrated by the engines which produce measurable power from a tea light candle in a well known competition.  Try that with a Rankine cycle! 

A Rankine cycle, while still described in terms of ideal processes, is a much more practical cycle as history has demonstrated.

There are several reasons why a Rankine, or normal steam cycle cannot match the efficiency of a Carnot cycle engine.  The boiler heat is not all transferred at a single maximum temperature.  Most is transferred at the boiler temperature then the temperature raised to the maximum which is only reached at the superheater outlet.  In fact, the heat transfer starts at the outlet of the feed water pump or feedwater heater, which further reduces the average temperature at which heat transfer takes place.  Then we force the heat transfer by a large temperature difference to achieve the required heat transfer from a small area.  This forcing produces vigorous bubbling and circulation in the boiler, which improves the heat transfer coefficient, but absorbs energy which cannot then be converted to work.  So it is nothing like an ideal reversible heat transfer process.

I don't think there is much more needs to be said about the Carnot cycle, however when it comes to engines, there are other ways to compare efficiency which I will introduce next time.

Thanks for dropping in

MJM460

[MJM460]

Engine efficiency -

Last time I talked about Carnot efficiency.  While the cycle is impractical in terms of designing an engine, its strength is in indicating a theoretical upper limit to the power that can be obtained from any given cycle and its maximum and minimum temperatures.  I should have noted in passing that you cannot use a temperature lower than the surrounding atmosphere, unless you cheat by ignoring the energy necessary to produce that lower temperature.   Hence the usual minimum temperature is usually around 15 - 25 deg C, although you would have an obvious advantage if your engine is in Northern Canada, Siberia or even wintering down in Antartica.  Satellites in outer space have an even bigger theoretical advantage from this point of view. Of course for steam cycle engines, the freezing point of water provides another limitation on the minimum temperatures.  However for most practical applications, the lower temperature is pretty much fixed by our location on earth, and to get higher efficiency, we must go to ever higher steam temperatures.  A quick calculation shows why we need supercritical boilers to achieve anything near 50%

However engine manufacturers wanting to sell their product don't want their performance figures reduced by cycle conditions outside their engine.  So they like to advertise their machine efficiency by comparing with what an ideal machine could do based on the same inlet and exhaust conditions.  Now a suitable process for engine comparison is the adiabatic cycle.  Remember, no heat transfer in or out during expansion.  We can calculate the efficiency of an ideal adiabatic machine based on the actual inlet and exhaust conditions.  We then conduct a performance test for the real machine to determine its power output.  I have witnessed many compressor tests where the process is similar.  They go to great lengths to reproduce the specified guarantee conditions, though in the case of compressors, there are recognised procedures for producing equivalent conditions from which the performance at the real conditions can accurately be calculated.  This is done where for example the gas being compressed is flammable and it would be difficult to conduct the test safely on the test stand.  The the efficiency of the machine is the actual test result divided by the output of that ideal adiabatic machine and multiplied by 100 to express it as a percentage.  Real steam turbines are in the region of 80%, perhaps higher, especially for very large machines, but reciprocating machines, I don't have real information.  But our models?  I suspect friction is a bigger proportion of the potential output power in a model compared with a full size engine, so our figures are certainly much less.  This is often called adiabatic efficiency.

Remember that this approach required a test of the actual machine.  To determine the adiabatic efficiency of our model, we need to do a performance test.  This requires a load which we can suitably instrument to measure speed and torque, from which we can calculate the power.  We also need to measure the steam inlet temperature and pressure, and the exhaust pressure, and preferably exhaust temperature.  I generally run my engines unloaded.  The entire load is the internal friction in the engine.  I still have to make a suitable load to conduct a power measurement on a loaded engine.  Measuring rpm is easy with a digital non-contact tachometer which is readily available at electronics stores.  It may also be a suitable project for Picaxe or Arduino microprocessors for the electronics enthusiasts among us.  I think the best way to measure the torque is to use a little digital scale, which these days are available with a resolution of 0.1 gm.  But I still have to design a suitable machine.  The issue is easily understood from the earlier discussion on the torque produced by a reciprocating engine, it fluctuates.  In a single cylinder engine, from zero to double the average, twice each revolution.  I don't really believe the text book drag brakes can really give a meaningful reading without considerable damping.  I am thinking in terms of perhaps a model ship propellor in a container suspended on bearings so we measure the torque on the container rather than balance the whole boiler plant on a scale.  A little DC motor used as a generator may be even better, though it would still have torque fluctuations.  Perhaps it can be calibrated so the current and voltage output can be measured and power calculated.  Any suggestions for a practical small brake are more than welcome.

Next time a closer look at the adiabatic power output from typical model operating conditions.

Thanks for looking in,

MJM460

[paul gough]

Looks like you'll have to move from a classroom to a lecture hall soon! 9096 reads for 120 days, 75/day,(up from 66), thats a lot of bums on seats. Thermodynamics and associated goings on can't be as daunting or esoteric as might be thought. Beyond doubt now that this thread is providing succour to an enthusiastic and curious crowd. Bravo! Regards, Paul Gough.

[MJM460]

A short one today -

Hi Paul, thanks for those encouraging words.  Have we really been going 120 days?  Time really flies when you are having fun.  I do hope that everyone is enjoying the ride, and learning something as we go.  I know I am.

That may seem like a strange statement, but when you are used to having all the test results from a well instrumented test stand, and have real information from the machine designers, it is all pretty straightforward.  When you attempt to see what you can deduce about a model from some limited home instruments, it can be a different story.

I have available results from a few runs of my engines, but I have accumulated instruments as I went along, finding out what I need as I go, as we all do with our tooling.  So inevitably many of the test results are incomplete, however I do have some that allow me to deduce a surprising amount.  Grand father duties have kept me quite busy so I have been a bit slow doing the calculations.  But I will keep working at it.  I need to fill out a few extra lines in my steam table with some intermediate values.  Then with a few results from a simple model test, I will show you what can be done in the next day or so.  I can also see quite a test program as my next project.

Thanks for looking in,

MJM460

[MJM460]

An engine test

Hi everyone, calculations all sorted out.  On a model test, the actual work output is quite small as you would expect, but to calculate it requires subtraction of two much larger numbers.  Consequently the large ones must be as accurate as possible, and no short cuts or back of the envelope estimates allowed.  Regardless of accuracy, which is another issue for later, I now have a set of calculations using numbers from a test of my own engine and they all make sense.  So first, what did the test involve, what calculations are involved, then most importantly, what do they mean?

The engine for this test is my first slide valve engine, all to my own design including the boiler, though obviously the concept can hardly be claimed to be original.  It is shown in the attached picture, and there is another view in the engine show case from soon after I joined the forum.  It is 12 mm bore and 20 mm stroke, and double acting.

The boiler is methylated spirits fired, it is about 2 in diameter (a standard copper tube size), 200 mm long, with four water tubes underneath.  It has a sheet metal furnace casing made from tin plate cut from a large coffee tin as a trial run for my sheet metal skill development.  Obviously looks very rusty now, so not worthy of showing on this forum, which is why it is covered in the pictures.  A new furnace casing from stainless steel or brass is on the list, and it will be fitted with some insulation.  The steam outlet (3/16 in tubing), winds back into the combustion space where there are two full turns around the space before it exits the casing.  I fill the cold boiler through a funnel, and insert a plug which protrudes 25 mm into the boiler and carries a thermocouple for boiling temperature measurement.  From the temperature, I get the steam pressure from the steam tables.  With no feed pump, run times are limited, but I can calculate steam rates by weighing the water fill, and the water I extract with a syringe when it is all cooled down.  The fuel burns out before the water level gets too low.

The steam pipe connection the boiler to the engine is insulated with a silicone tape, and could be improved.  It has a displacement lubricator and a thermowell for a thermocouple on the engine inlet.  The exhaust outlet also has a thermowell so I can measure the steam inlet and exhaust temperatures.  It then has an oil/condensate separator with a drain that I have described previously, and a vertical exhaust stack.

The burner is perhaps described as a semi vapourising type, something along the lines of a Trangia camp stove burner, a bit more vigorous than wicks, but needs development to get a bit more heat.  I would like to build one of the so called silent types, but apparently everyone knows how to do that so they are never described in articles or books that I have read, and I still don't know how.  The burner tank holds about 50 ml of Meths, and I calculate the quantities by weighing before and after a run which is just over 20 minutes from light up to extinguished.

I use the kitchen digital scale (resolution 1 gm.) for weighing water and fuel, a multimeter or two with thermocouples for temperature and the most recent addition, an electronic temperature meter with no voltmeter functions, but it has two thermocouple inlets which I can read either one at a time or as a difference.  Even to 0.1 degree, if I could get the rest of the procedure sufficiently repeatable.  I also have a non-contacting infrared thermometer which is good for comparative readings around the place, and a non-contacting digital tachometer for engine rpm.  The missing item is a means of measuring torque.  However that is not required for the test I am describing.  The engine is just free running without any external load.

I will come back to accuracy another time, just using the readings as they come so far, to see how the whole setup works.  Though I have compared the thermocouple readings at the ice point and boiling point and they are looking pretty good.  Readings are generally passing the "looks reasonable" test, and some consistency checks, so I think quite adequate for illustrative purposes.  Better accuracy can come later, but a few more repeat runs to ensure the results are repeatable is probably the main requirement.

To conduct a test, I fill the boiler with a weighed quantity of water, and fill the fuel tank which I also weigh.  Tighten the plug, set up the thermocouple instruments and record the time when I light up.  The boiler temperature takes about 6 min to get to 100 C.  No cylinder drain valve on this one, so I gently turn the engine over by hand to blow out the condensate which heats the cylinder while the boiler temperature rises.  Within about a minute, the engine runs up quite nicely and shortly after the boiler settles at about 116 C which the steam tables tell me corresponds to 0.175 MPa absolute, or about 75kPa gauge.  For the metrically challenged, this is about 10.9 psig.  At this pressure the engine runs at about 1100 rpm.

Nothing unusual in any of that, except perhaps for the instruments.  But it is probably worthwhile describing it so you can see the areas where compromise and approximations are necessary.

My notes say I filled the boiler with 200 g of water and extracted 58 g after it cooled, so 142 g evaporated.  Similarly 42 g of fuel used.

From light up to engine running was 6 min 40 seconds and I extinguished the flame after a further 8 min of engine run time.

I read the boiler temperature, engine inlet and exhaust temperatures and engine rpm often enough to judge typical figures, and runs seem pretty steady.  So I have extracted the following -

Boiler temperature 116 C.
Engine inlet 138 C
Engine exhaust 104 C
RPM 1100

It doesn't look like much but you may be surprised to find out what it can tell us.  Next time I will use these figures to get a picture of the engine thermodynamic performance.

Thanks for looking in

MJM460

[MJM460]

Some calculations -

The test was actually done some time ago.  Now you have an idea what was involved, and we have some results, so time to set out some calculations. 

Now don't be too intimidated by that, they are little more than simple arithmetic.  A bit tedious to do by hand, but when I started, I had no computer, and in fact no calculator.  And no, I am not that ancient.  I had a slide rule for multiplication, which together with a pencil and paper is enough, but I suggest trying that way these days is wasting time that could be better used making swarf.  In fact, the calculations are quite repetitive, so the best way to do them is in a spreadsheet.  Once we work out the formula once, it is copied, then pasted into each place it is needed.  The only trick is what calculations to do, and finding meaning in the result, and that is what this post is about.  Well perhaps this one and one or two more.

We will use the first and second laws of thermodynamics, and here is where we find the usefulness of those calculated properties, enthalpy and entropy that we discussed earlier.  With the measured results, specifically temperature, we can look up the other properties in the steam tables.  The tables list properties on a " per kg" basis, or per lb if you are using imperial tables.  We then multiply those values by the steam and fuel rates of our engine.  So let's work those out first.

The fuel burned was 42 g in 14 min 40 seconds, this is an average of 2.86 g/min or 0.0477 g/s.

The heating value of the methylated spirits is 26000 kJ/kg.  This is the lower heating value as it assumes the water produced as a product of combustion is not condensed, but goes up the stack to atmosphere as steam.  As an aside, it allows for commercial meths, in this country anyway, being 5% water, and this water must also be turned into steam, and also the vaporisation of liquid meths, which only burns as a vapour.  So we can multiply the heating value by the consumption rate to get the energy input into our boiler.  Now for model purposes, kg and kJ are very big units and all the calculations are cluttered by too many zeros.  So note that 26000 kJ/kg is the same as 26000 J/g.  Then 0.0477 g/s x 26000 J/g = 1240 J/s or 1240 watts is our heat input from the fuel. 

Now, I usually assume that this average is also the uniform rate of fuel consumption, a bit rough, but I have checked by stopping when steam pressure is achieved, extinguishing the flame and reweighing the burner.  It seems about right based on that point anyway.  More complex to design an experiment to give more detail.

We can also estimate the steam production rate.  Remember that steam production started after 6 min 40 seconds.  The heat during this time goes into heating the water, the boiler shell and the furnace.  We could calculate the heat required for the water and the boiler shell separately, but it is not of major interest, but once these items get to steam temperature, they don't absorb more heat, so we can ignore them and assume the remaining heat goes into steam production, and all the steam produced is produced in that 8 minutes of engine running.

This does not all go through the engine as some is condensed in heating the piping and cylinder, but it left the boiler as steam, so it is still steam production.

We had 142 g of steam produced in 8 min, so if we assume  an even rate we have 17.75 g/min or 0.296 g/s.  Given the assumptions, I probably should have called it 0.3.  Certainly three significant figures is not justified, but it helps with making calculations consistant.

With these basic measurements that we can all do, we already have a rate of fuel consumption, boiler heat input and steam production.

The next step involves looking at steam tables to determine the enthalpy and entropy of the steam.  From these we can then work out the boiler efficiency from how much heat from the fuel ended up as energy in the form of steam, and we can calculate the work an ideal engine would produce, and even how much work our engine produced, though that requires further explanation later.

The steam tables I have do involve quite large steps, so they do not have the precise temperatures or pressures that my boiler is operating at.  Steam properties are also published in graphical form, a common one using temperature and entropy as the axes.  Another uses enthalpy and entropy, and some even use pressure and specific volume.  They are hard to use with any accuracy, but they show the general trend of the information.  A close look at any of these will show that most properties appear as curves, with the only straight lines appearing in the two phase region where liquid and vapour both exist in equilibrium.  Fortunately, when finding the value of properties between the ones tabulated in the tables, it is normally considered accurate enough to assume the properties are linear between any two consecutive listed values.  This means we can use a simple linear method to construct a table with the additional values we need.

The boiler temperature of 116 deg is actually listed in the pressure tables, (well actually 116.06, but surely close enough) where the equilibrium pressure is 0.175 MPa.  Yes the tables uses MPa instead of kPa, however it is easy to multiply the small numbers we need by 1000, so no real problem, and no interpolation needed.  We can directly see the enthalpy, (and entropy of we needed it) of both the saturated water (hf), and the saturated steam (hg) at this temperature and pressure.

The pressures are absolute, so 0.175 MPa is 175 kPa absolute, say 75 kPa(gauge).  For the metrically challenged, about 10.9 psig.  The boiler is good for 700 kPag, and in any case has a properly set safety valve which I ease with the pliers before starting, so no problems there.

So my boiler temperature tells me the steam pressure in the boiler is 75 kPag, and the air, which causes additional pressure is soon expelled as soon as I let a bit of steam out of the boiler.  Still a gauge would be nice to have.

Next we have the engine inlet temperature of 138 deg C.  This is after the superheater, (actually even after the steam pipe and lubricator) and so we have at least 22 deg C of superheat for those who thought our super heaters were little more than driers.  You will see that it is enough to be useful.

My superheated steam tables unfortunately do not include 0.175 MPa, nor do they contain 138 deg C.  As well, they are in deg C not K, as 138 deg C is 600 K, and that might have been included.  You might be luckier when you do a test.  Worth finding tables listed each way if you come across them.  This means we have to interpolate the superheat tables, first to get a table for 0.175 MPa, then again to get values for 138 deg C.  Not very easy to work to a desirable superheater outlet temperature, as it would require adjusting the length, and even then would probably not achieve the same result at another boiler load or firing rate.

This might all be a bit tedious for those that already know how to do it, but I want to bring along those that have never used a formula in a spreadsheet as well, so please bear with me.  But enough words this time and interpolation next time

Thanks for looking in patiently.

MJM460
 

[paul gough]

A typo that might confuse a novice from paragraph on heat input from fuel. "So note that 26000 kJ/kJ is the same as 26000 J/g." Regards Paul.

[MJM460]

Thanks, Paul.  Well spotted. 

I read it all at least three times, but things still slip through.  Often Apple makes very puzzling corrections, but that one was surely all my own work.   Assistance in finding these things is always welcome.

It is now corrected.

MJM460

[steam guy willy]

I notice the exhaust pipe is also lagged ,Is that so you can collect the condensate from the bottom of the chimney ??
Willy

[MJM460]

Interpolation

Hi Willy, welcome back.  I hope the show went well.  Two reasons for the exhaust pipe insulation.  First, it reduces the risk of burning my fingers, it is still over 100 C.  Second, quite the opposite of collecting the condensate, it reduces condensation in the exhaust pipe, so the vent steam is more dry, and so less hot  droplets raining down.  The dry steam soon mixes with the air and is dissipated before it condenses.  Remember that condensation involves rejection of heat, the opposite of evaporation in the boiler.  On the other hand, the oil does drop out in the separator and seems to mostly end up in the drain tin.

Following on from yesterday, we need to do three interpolations of the steam tables to get values for the missing temperature at the missing pressure, but it's not too hard with a spreadsheet.

I start by putting the missing temperature into the nearest two pressure tables in the superheat section of the steam tables, that is 0.1 and 0.2 MPa.  So let's start with the 0.1 MPa table.  In my table the nearest temperature below 138 is 100, and the nearest one above is 150 deg C

I set up a little table like this in my spreadsheet-

T1,  v1,  u1,  h1,  s1
Tx,  vx,  ux,   hx,  sx
T2,  v2,  u2,  h2,  s2

Please read the 1, 2, and x as subscripts, and obviously T1 is 100, v1, u1, h1 and s1 are the values at 100, Tx is 138 and the x subscripts refer to the values at 138 which so far are unknown, and the 2 subscripts refer to the values at 200.  Now, I transcribe the known values listed in the tables into just this small table.

Then I construct a formula for finding ux.  (I will get back to vx shortly)

ux = u1 + (Tx- T1)/(T2- T1) x (u2 - u1)

I type this formula into the cell for ux in the spreadsheet and when it is complete, I exit the cell.

Remember in a spreadsheet, a formula starts with an "=" sign.  You select the cells you want to use with the mouse and the spreadsheet will insert the cell reference rather than the number within the cell.  Use all the signs, including brackets, but no spaces.  In Excell, Open Office, and others you exit the cell by pressing enter.  In Numbers, on an iPad with a touch screen, you touch the green tick.  And the answer appears in the cell as the number you are looking for.  Obviously it should be a bit above 1/3 of the way between the values for u1 and u2 as a rough rationality check.

If you are not familiar with the procedure it may seem a bit tedious, but now comes the powerful bit.  You can copy that formula and paste it into as many places as you wish.  But there is more, as they say on TV.  The spreadsheet shows the cell references for the cells you select, perhaps B3 etc., but it remembers them as relative positions, eg cell above, cell below, cell two to the left etc. from the formula location.  This means you can copy it to another place, providing all the cells you want are in the same relative locations.  But you can change this by using absolute references.  This is indicated in Excell by a $ sign.  You can do three things.  With one $ sign $B3 means always column B, but the same row relative to where our formula is located.  B$3 means always row 3 but the same column relative to the formula cell location.  Then with two $ signs, $B$3 means always cell B3, regardless of where on the spreadsheet the formula is located.

In this case, the temperatures are always in the same column regardless of whether we are calculating v, u, h or s, so the cells in the formula which refer to a T1, Tx or T2 need to be edited with $ signs to fix the column, for example $B3.

I can now copy my formula for ux and paste it into the cells for vx, hx, and sx, and job done.

You may have noticed that v is smaller at T2, while all the others are getting bigger.  The same formula is used, the required negative sign is already there in the term (v2-v1) as v2 is the smaller value, so no problem at all.

Now the same process to insert a 138 deg row in the 0.2 MPa table.  Then I set up a third table consisting of the two 138 deg rows just found, and with the pressures 0.1, the required 0.175 and 0.2 in the first column instead of temperatures.  With the pressures in this location, the formula remains the same, so I can copy and paste the same formula into this third table, and I now have the table I need for 138 deg C and 0.175 MPa.

I hope that if you have been reluctant to use formulas in a spreadsheet, you might now feel encouraged to try.  That first one may well have taken longer than a pencil, paper and a calculator, but in this exercise I copied that formula, then pasted it 15 times with 15 mouse clicks and job done.  All of a sudden the initial time was well spent.  (The extra four were for that 104 deg exhaust temp.). Don't hesitate to ask a question if this is not clear.

So here is what we have so far -

Boiler 116 deg, water and vapour together means 2 phase region, so use saturated steam pressure table which gives P = 0.175, vf = 0.001057, vg = 1.1593, hf = 486.99, hg = 2700.6, sf = 1.4849, sg = 7.1717

Engine inlet 138 deg superheated, pressure assume equal boiler pressure = 0.175 MPa, interpolation gives v = 1.167, h = 2745.91, s = 7.3018.

Engine exhaust 104 deg, p = 0.1 MPa ( actually atmospheric, assumed 100 kPa), v= 1.72, h = 2684.2, s = 7.380

Units, Pressure MPa, (= 1000 kPa), specific volume, v, m3/kg, enthalpy, h, kJ/kg (= J/g), entropy, s, kJ/kg.K (= J/g.K).  K is for Kelvin, the absolute temperature unit for metric units.

Well, that is the tedious part, we have the figures for both steam rates and steam properties, but what do they mean, and what can we learn from them?

Next time, I will apply the first and second laws of thermodynamics to the boiler and to the engine for some interesting and even surprising results.

All eyes open for any typos that need correcting please,

Thanks for looking in.

MJM460

[MJM460]

Calculated Steam properties for test and Boiler performance -

Another small correction to the post about two days ago, the total fuel burning time was actually only 14 min 40 seconds, so the fuel burned was 0.0477 g/s and the heat released 1240 watts.  I have now corrected that post.  Another case of old eyes dropping a line, or something like that.  Please let me know if you see any others.

All of those figures we gathered in the last post can be a bit daunting and hard to picture, so it will be helpful to portray them graphically.  All our readings were actually temperature, so we will use that for the vertical axis.  The second law will have us looking at entropy, and it will be useful to have that as the second (horizontal) axis.  This Temperature - Entropy diagram is quite commonly used to portray a plant cycle.  Pressure, specific volume and enthalpy can then all be shown on the diagram, but better not add too many or it will get very cluttered.  You can also illustrate your cycle on pressure - volume or even enthalpy - entropy if that makes things clearer to you.

I have hand drawn the diagram attached, but tried to keep everything in the correct relative positions.  The bell shaped curve is the boundary of the two phase area where water can exist as liquid and vapour at the same time.  It is bounded by a horizontal straight line at the bottom below which water will be solid.  To the left of the curve, water is liquid, and to the right, vapour.  Above the top of the curve, called the critical temperature, which has only one pressure, the critical pressure, water changes from clearly liquid on the left, to clearly vapour on the right with no clearly distinguishable boundary between, unlike the distinct liquid, vapour two phase region that we are so familiar with.  I should point out that the peak of the bell curve is not correctly shown in proportion, it should be at 22.09 MPa and 374.14 C, the critical pressure and temperature for steam.

I have drawn the constant pressure lines at 0.175 MPa and also for 0.1 MPa to illustrate our steam plant process.  The 0.175 line should extend to the left and down to room temperature, but that part is only important before we start generating steam, the heat up period, which was about 6 min 40 seconds.  So point 1 is the saturated water at vapour pressure for 116 deg C.  Point 2 is the saturated vapour condition, steam 116 deg C just at the point superheating starts.  Point 3 is actually the engine inlet, but I am assuming close enough to the superheater outlet, as the line between is insulated.  Point 4 is the engine outlet temperature measured in the test.  We cannot easily calculate this condition, it can only come from a test.  In full size, the manufacturers have some pretty good computer programs, so they can predict the performance for guarantee purposes, but in the end, those programs contain an efficiency which comes from a large number of previous test runs of similar engines.

So the obvious question, how have I arrived at points 4 and 5?  Let's look at the thermodynamic analysis of this process.  For the boiler, the first law says Q = h3 - h1.  That is, the heat transferred into the boiler during steam production is equal to the difference in enthalpy between the superheater outlet and the saturated liquid point.  I will come back and put some figures in that shortly.  Then for the engine, where we want to determine the work output of an ideal adiabatic engine, the second law of thermodynamics says s5 = s3 for an ideal adiabatic engine.   An adiabatic engine is used as our standard for comparison because no real engine can produce more power than an ideal adiabatic engine.  I know the exhaust pressure of both the ideal engine and our model, it is open to atmosphere, so it is atmospheric pressure.  In a perfect world I would have measured it with a calibrated barometer, but I didn't, don't have one, so I am assuming it was 100 kPa (absolute) or 0.1 MPa.  Two independent properties are enough to define all the properties of steam using the steam tables. 

Note that point 5 is shown inside the two phase region.  The value of entropy from point 3 at 0.175 MPa, when applied to the 0.1 MPa line in the steam tables confirms that to be the case.  In that area, temperature and pressure are not independent, as the is only one possible pressure for each pressure where liquid and vapour are in equilibrium.  However, temperature and entropy are independent so are sufficient to completely define the steam properties.

On the engine exhaust, I only measured the temperature.  However, the pressure is the same as at point 5, at atmospheric pressure, i.e. 0.1 MPa, where the saturation temperature is known at only 99.6 C, so our measured temperature of 104 deg means our actual exhaust is superheated.  In that area, pressure and temperature are independent, so sufficient to completely define the steam at the exhaust.  You will notice on the diagram that my engine exhaust is shown with higher entropy than it had at point 3.  The second law says that no engine exhaust entropy will be less than the inlet, and only for an ideal reversible engine, will it be equal.  For all real engines, the exhaust entropy will be higher than at the engine inlet.

For the purpose of calculating engine performance, I need to calculate the enthalpy at points 4 and 5.  The first law of thermodynamics says for the ideal engine, W = h3 - h5, and for my real engine, W = h3 - h4.  That is the work output equals the difference in enthalpy between the inlet and the exhaust.  We can perhaps accept that for the ideal engine by assuming no friction, but our real engine requires further explanation.  We will get to that later.

Now we have all the information we need, and have defined our method, so let's put in some figures.

For the boiler, the heat input h3 - h1 = 2745.91 - 486.99 = 2258.9 kJ/kg ( or J/g).

My steam production rate was 0.296 g/s, so heat in the steam = 2258.9 x 0.296 = 668 J/s = 668 Watts.  I can compare that with the heat from the fuel burned, which was 1240 watts.  I can conclude that 668 J/s of that heat was transferred into the steam, the rest was lost partly up the stack, and partly through losses from the boiler casing.  That means a boiler efficiency of 54%.  I think perhaps acceptable for a simple boiler.  I was hoping for a bit more.  Perhaps I will be able to improve it with some casing insulation, and perhaps some experimenting with air flow.  In another post, I will look at the heat transfer surface area and see if I can calculate a steam production per unit of surface area to compare with what K. N. Harris suggests.  I suspect it will be lower than his as I think he assumes coal firing, which I would expect to produce a much higher temperature than my small Meths burner.

Surprising how long it takes to describe some of these things.  I hope it is sufficiently clear to illustrate the procedure, and provide enough guidance for anyone who would like to do such a test on their own engine.  Please ask if anything is unclear.  Now I think it's time to take a break, and calculate the performance of that ideal engine next time.

Thanks for looking in,

MJM460

[paul gough]

Now this is really interesting stuff!!! These numbers start to give me a ball park notion of what might be going on in my tiny Lion boiler and give me more inspiration to clamber up the learning curve. Unfortunately my computer skill ,(I don't have any), doesn't include spread sheets,  so I'll have to fall back on the old laborious ways to work things out when I master the methods. I remember many many decades ago when I was involved in Herpetology and running around sticking quick acting thermometers up tiger snake cloacas trying to determine their preferred body temperature we were lent some thermocouples and a millivolt meter from the uni. Less intrusive for the animals than a glass tube and made the job a little easier. These thermocouples were hand made by the techy at the uni., I think they were silver and something and was wondering if you knew of the metals used in the ones suitable for our steam temperature ranges. It might be possible for model engineers to make them?? Looking forward to the results on the engine. What a great thing it would be if a whole bunch of people rigged up their models and took some measurements and analysed them, maybe some interesting things might result from a broad investigation on our small sizes. Especially things like the effectiveness of lagging, its minimum thickness etc. etc. Regards Paul Gough.