Author Topic: Talking Thermodynamics  (Read 154540 times)

Offline MJM460

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Re: Talking Thermodynamics
« Reply #180 on: July 28, 2017, 11:37:39 AM »
I hope my discussion on entropy yesterday was enough for our purposes, as it did not allow me to continue looking at yesterday's other questions.  So today, Paul's question on the molecular interaction that produces force on the piston.  Paul, you have quite properly observed that while I described the action of the gas molecules in detail, I treated the piston more superficially as though it was a uniform solid.  The only thing I can say in defence is that there are good precedents for this approach.  However, it is not necessary to simplify, as treating the metal piston as jiggling molecules is quite valid, it just adds another layer of detail, and does not change the original conclusion.  It is all about scale of the motion and particle mass.  You will remember that gas molecules move at high velocity in all directions.  The velocity on average is enough that the molecules easily escape the close range attractive forces any time they come into collision with another.  I remember looking up the mean free path and it's very large compared with the size of the molecules, but unfortunately don't have access to the book at the moment.

On the other hand, the metal molecules have much less energy.  Obviously not still in the vapour state, or even liquid.  Molecules are still moving but the energy is so low that they are well in the grip of the short range attraction forces.  Their energy and hence velocity is so low that they have  dropped into a regular close packed pattern that can actually be identified by X-ray diffraction techniques and in a larger scale, in the crystal structure.  The molecules are still moving in this array, they cannot "clump together" as when the molecules get very close together there are repulsive forces.  But there is not much room between the jiggling molecules of a metal that gas molecules can penetrate and get lost in the metal.  Not much room, but not no room.  There are some gaps or faults in the regular structure that make grain boundaries in all but very carefully produced single crystal structures.  A few gas molecules sometimes get trapped in these gaps, particularly small molecules like hydrogen, and this can cause problems in welding the affected metals.  But solubility of gases in metals is much less than in liquids for example.  In addition most practical piston metal atoms are much heavier than gas molecules.

So what happens when a gas molecule collides with the metal surface?  First it approaches a nearly solid wall of vibrating metal atoms, that are moving in a tightly packed array.  Even if a gas molecule penetrates the first layer, I am guessing it does not often get through the second without colliding with one.  Of course the motion is all random so the gas molecule could collide with one moving towards it, or one moving away, or like billiard balls it could hit at an angle.  The metal atoms are on average all moving in one direction that we identify as the piston movement.  But at each collision, conservation of momentum applies as a basic law of physics.  It is the physical law behind Newton's law about bodies continuing to move unless acted on by an external force.  Unlike energy, there is no equivalent of energy conversion with momentum.  Conservation of momentum can be applied separately in each of three perpendicular directions, though only components in the direction of piston movement is of interest in production of work.  The law of conservation of energy still applies, but the sum of the energies of all the particles will be less after the collision, some does the work to accelerate the metal atom and some is converted to heat.  So conversation of momentum is easier to apply in this case.

It is worth noting that in addition to conservation of momentum, which should probably be called linear momentum, there is an analogous law of conservation of angular momentum.  This applies to the spin motion of a particle, again it applies to spin around three perpendicular axes.  The formula for angular momentum are very similar to those for linear momentum, just angular velocity and torque instead of velocity and force.  And moment of inertia, instead of mass.

So the gas particle bounces back into the gas space as it still has too much energy to be captured by the close range attractive forces, and the space between gas molecules is enough for it to be hardly noticed.  But what about the metal particle?  Well it bounces off on the opposite direction, back into the metal.  Much lower velocity as it is so much heavier than the gas molecule.  Also it is in a close packed array so as soon as it tries to move beyond it own little space, it collides with another molecule, which collides with another and so on right through the metal, and can be seen in movement at the other side millions or is it billions of atoms away.  But the close range attraction prevents the last particle popping out the other side.  So the solid piston acts like, well, like a solid.  The net force due to all this change of momentum on the top and bottom face of the piston is carried through to the crank pin where it produces torque as I have already described.

I have probably still glossed over a few details but I hope that is enough to illustrate that the molecular motion model is still valid when you include the molecular model of the metal piston.

I think the next question was about how the structure of the molecules affects the collisions, compared with solid billiard balls.  Of course solid billiard balls are a concept that most if not all of us are familiar with, even if some have invested more time in study of the billiard table than others.  Atoms, however, at a first level of detail, consist of a positively charged massive nucleus, surrounded by a cloud of negatively charged orbiting electrons, each with relatively little mass.  And mostly empty space between.  So what does a collision look like at this scale?  Well I am not a physicist, so I am not sure that I can give a definitive model.  However I would think that the strong close range repulsion forces, possibly something to do with the positively charged nuclei, might mean that the collision involves elastic forces strong enough to look like reaction of elastic solid bodies.  But it would need some detailed study of molecular physics to be sure.  Perhaps some holiday reading to look out for.  Of course it is even more complex when, instead of single atoms, we have molecules.  For example oxygen and nitrogen both involve molecules consisting of two atoms, while water has one oxygen and two hydrogen atoms, hence H2O.  These combinations mean we have atoms that are not at all like a spherical ball.  Their asymmetrical form would have some influence on the energy contained in the spin around each of the three perpendicular axes, and also the momentum change when they collide.  And of course the molecules implies another energy change in a chemical reaction which involves molecular chemistry.  Again well out of my field.  Personally I am happy to stick with the simpler assumptions, I think they give enough information for my purpose.  But I recognise that as a gap in my knowledge.

There is one other issue in the molecular model.  A characteristic of the random motion of molecules is that the magnitude of the velocity as well as the direction is random.  This means that there are large numbers of molecules with velocity well above and others well below the average.  But is is reasonable to discuss on the basis of an effective average.  Studying at this level of detail is however a whole new field. 

The other outstanding question was about the elastic properties of metals and how these affect our selection of a piston material.  I wanted to start this one from the point that all materials deform under stress.  In simple language they compress or stretch like a spring.  Just some deform less than others.  Also some are quite linear and steel is in this category, some less linear.  When the material is deformed an elastic material returns to original form when the force is removed.  There is usually a limit beyond which the deformation becomes plastic.  That is the material does not return full to the original shape.   Selection of material involves not only consideration of strength, but also temperature resistance, chemical resistance, wear resistance, friction and so on, and also consideration of manufacture such as machinability.  Availability and machinability are probably among the first priority for model engines.  All the commonly used piston materials have slightly different but adequate modulus of elasticity and strength, although care over specific choice of alloy is necessary if aluminium is required for higher temperature applications, due to both strength and thermal expansion.  Basically the differences in modulus of elasticity is not very important in the conversion of energy to work.  Thermal conductivity is important for heat transfer applications, and also when thermal insulation is required, but again not in pistons.

I hope that deals with some of the philosophical issues, next time back to those engine questions from Paul and perhaps Willy's air in the boiler issues.

Thanks for following,

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

Offline paul gough

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Re: Talking Thermodynamics
« Reply #181 on: July 28, 2017, 01:27:21 PM »
Thank you very much for this extended trip to the interface where the molecules interact. It has cleared some of the fog and settled my thinking as I am now comfortable that we have treated steam and steel (our piston) as equals, molecularly speaking. Your explanations have given me a pretty precise 'picture' of the actions of molecules on the piston from a macro and microscopic perspective. Now I need to get comfortable with all the thermal or heat energy issues. This I think will be very energetic mental exercise and hope my brain does not pass through some super critical phase and end up suffering runaway entropy!

Looking forward to seeing your thoughts on the model cylinder materials/construction. Regards, Paul Gough. P.S. I just noticed the average hit rate to this thread, (approx. 6000/90 days= 66). This would seem to me to be very satisfying to have a packed classroom every lecture!
« Last Edit: July 28, 2017, 01:36:45 PM by paul gough »

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #182 on: July 28, 2017, 03:09:11 PM »
Hi..........I have just had an eureka moment and now realise that the study of Thermodynamics was to determine how long a steam engine engineer could have for a tea break !!!However this was before they invented stainless steel teaspoons !!!!

Offline MJM460

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Re: Talking Thermodynamics
« Reply #183 on: July 29, 2017, 12:29:48 PM »
Hi Paul, I am glad the explanation on gas collisions with the metal surface made things clearer for you.  You know, brain meltdown depends not on energy, but on rate of energy movement, or power.  Energy is measured in Joules, J, while power is joules per second, J/s, also named Watts. So to avoid the brain meltdown, it is a case of pacing yourself. I think that was your words very early in the piece?  However the main thing is that we make it interesting and preferably also useful.

Now you were asking about cylinder arrangements for your little locomotives, so let's discuss the cylinder after all that talk about pistons.  In principal, the cylinder is only there to complete the enclosure around the piston so the steam is constrained and the high pressure can act on the piston.  Of course, when the pressure causes a force on the piston, there is an equal and opposite force on the head of the cylinder.  The magnitude of the force is P x A, and the direction perpendicular to the cylinder head.  Remember to use consistent units, so pressure is Newton/square metre, or Pascals, and area is in square metres.  Then force is in Newton's.  This force has not been mentioned so far as the cylinder head on a stationary engine is by definition stationary, meaning that it does not move in response to the force, and hence does no work.  Remember work = Force x distance.  If distance = 0, then work is zero.  So what happens to the force?  The force is transferred to the frame through the cylinder mounting fastenings, and is resisted by the main bearings.  And of course the big end bearing is providing an opposite force on the main bearings, so the whole lot is in equilibrium.

This is a very important point in the engine design.  The primary strength design of the engine is based on the magnitude of this force.  The cylinder head bolts must carry the load in tension, the cylinder mounting bolts must carry the load in shear, or there may be a shear key to transfer the load to the frame.  Similarly for the main bearing mounting.  On the piston side, the force is carried through the piston rod, and with some allowance for the angulation, through the con rod.  It is a major factor in the bearing design.  There must also be an allowance for inertia loads, and bending moments, when things are not in line, but the basic rod load or cylinder head load is the basic design load.  My compressor experience tells me that major manufacturers design a model series around nominal steps in rod load capacity and design the frame and motion parts from that, rather than start from scratch every time.

Thermodynamics assumes that expansion in an engine is a nominally adiabatic process, meaning no heat transfer in or out.  This assumption is used almost entirely because it makes mathematical analysis possible, not because it represents reality.  The performance of a real engine is determined on a test stand and compared with the ideal adiabatic engine.  So what is the effect of the heat transfer on engine performance?  Now heat input hardly ever happens so let's deal with that first.  I have not been able to quickly find an example with the first law equation for this example, and I am not going to try and derive it.  However basically it says that Heat input = change in internal energy plus the work done.   We don't know how much of the heat goes into internal energy and how much goes into work output.  So let's put together a few things.  The analysis of an ideal adiabatic process assumes the process proceeds through a series of very small steps.  And the first law applies to each of these steps.  The work output is pressure times area times the distance the piston moves in each tiny increment.  So the heat probably goes mostly into internal energy, but that will be reflected in the pressure for the next increment.  So the pressure does not drop as much as you would expect in that increment with the consequence it is higher for the next increment, which means some more work produced.  I don't know how much more, but directionally, heat input to the cylinder during expansion will increase the engine output.

In a real steam engine, the more likely position is that heat is lost from the cylinder.  We know the outside of the cylinder is hot, so it will loose heat to the air, and that heat comes from the steam.  Applying the same logic we can see that in this case, the heat loss reduces the engine work output.

Now to think about how we can use this information for your engines.  First, we can at least reduce the heat loss by adding insulation, or cladding to the cylinder.  This is done in many of the model builds on this forum, reflecting the fact that this was indeed full size practice.  Relatively simple step that adds to appearance and directionally improves the engine output by reducing losses. 

In the early days, when engines operated at very low pressure, some went a step further and tried adding a steam jacket around the cylinder.  This obviously adds a level of complexity, but the question becomes where should the steam come from?  You might be tempted to say what about recovering heat from the exhaust steam by using some of it in the jacket.  Now remembering that heat moves from a high temperature to a lower temperature, and as the exhaust temperature is lower than the average temperature in the cylinder, it will not actually provide any heat input.  However, it means the temperature difference driving the heat loss is the difference between the cylinder temperature and exhaust temperature, say 100 deg C, compared with say 20 deg C atmospheric temperature.  So there would be less heat loss, even though no actual heat gain.  If we use some of the engine supply steam in the jacket, we now have a small heat input to the engine.  However I feel that on balance of probability, that steam might produce more work if used in the engine.

I don't know how much extra power is produced by reducing the heat loss.  If we think about Willy's electric heater of 500 watts, similar in magnitude to my methylated spirits burners which produce about 600 watts, you engine burner might be similar.  I suspect the engine output from such a boiler might be around 2 to 5 watts.  If we made a dynamometer and did an engine test, we might expect to identify a difference of say 5 to 10%.  A full size test stand only achieves around 1% accuracy, so I doubt we would do better.  I don't know if the difference would be measurable, but race winning performance is certainly achieved by tiny differences, so it is probably important if we want to achieve the best we can.  At the very worst it will only help us avoid one source of burned fingers.

But what about the question of a solid block compared with a light weight fabrication?  Before we try and answer that, there is another temperature variation in the cylinder wall when the engine is running that we should be aware of.  At the beginning of the power stroke, hot steam from the boiler superheater is admitted to the cylinder.  This will tend to lose some heat to the cylinder, causing some loss in efficiency as we have discussed.  Then as the piston moves down, and the inlet valve closes, the steam starts expanding.  In expanding without heat input, the steam cools, so that it is close to exhaust temperature at the bottom of the stroke.  Then the exhaust steam is pushed out at the top of the cylinder cooling it.  So in each cycle, the cylinder is repeatedly heated and cooled, clearly a heat loss that leads it loss of efficiency.  It also causes a little variation in thermal expansion, which may in time lead to sealing problems with the  head gasket, just conjecture, I don't know if the movement is enough to cause such problems.  This temperature cycling occurs under the insulation, whether insulation is present or not.  It is probably the clue to the answer on whether to use a lightweight fabrication.  A more massive block provides a thermal inertia which would tend to stabilise the temperature a bit which may be helpful.  And a bit of mass generally helps with traction in a small engine, so I would probably lean towards a solid block (with insulation around it, rather than a very lightweight fabrication.  That also appeals to my skill level with soldering as I currently need to borrow a big enough burner, preferably with operator attached, for anything of significant size.  It think it would take some experimenting and very careful observation to determine if there is a real difference in performance.  Of course a solid block will absorb more heat on startup and hence produce more condensate initially, but once everything is warmed up and running it would not make any difference to condensate in the exhaust.  I suspect the choice will probably be determined by ease of manufacture and availability of material, rather than thermodynamic considerations. 

Similarly with material choices.  Compatibility between the piston and cylinder materials is probably the main consideration.  Thermal expansion needs to be considered.  I suspect an aluminium piston might seize in a cast iron cylinder, while a cast iron piston in an aluminium cylinder might leak excessively.  So it is worth thinking about whether the clearances in your engine will increase or decrease when it heats up.

Thanks for pointing out the viewing numbers.  I hope it means that there is interest in the topic, and assume that others will join in at the appropriate time if they would like to add something, or clarify something.  I am not a teacher or lecturer, and you can probably tell from some posts that I was not any loss to that profession, I am just trying to pass on some things I learned in my career in the hope that it will be helpful.

Next time Willy's questions about air in the boiler.  By the way Willy, we are all waiting for your posts of the cooling curves you get with and without the teaspoons in your tea.

Thanks to everyone for reading,

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #184 on: July 29, 2017, 01:10:03 PM »
Thanks for this latests info,.....as the cylinder block expands should the holes in the frames be slightly elongated away from the middle bolts so there is no shearing stresses on them ? or even worse could it distort the frames, especially if it is a solid block??can one work out the actual length increase for a freezing cold cylinder block, (early in the morning) to when it is working at 250 LBS/s   16 Bar later on in the day half way to Scotland from london ? All these forces are ones that we don't usually think about.!! They say that you can suspend a London bus from a 1/4" bolt!! but i am not sure. I shall endeavour to do that experiment soon...promise...I have just found some graph paper in a skip ! so that has prompted me !! Ok I have a   K.type thermocouple ? and i might use it on the Foreignhight scale as it will be more sensitive !!
« Last Edit: July 29, 2017, 04:50:01 PM by steam guy willy »

Offline MJM460

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Re: Talking Thermodynamics
« Reply #185 on: July 30, 2017, 12:22:37 PM »
Hi Willy,  you are quite right to point out that I stopped the discussion on cylinder construction a bit early, and expansion and how to live with it should have been included.  I quite deliberately say how to live with it, rather than control it because we basically have nearly no choice.  If you heat steel, it expands.  If you try and restrain this expansion, you will encounter tremendous forces as you would have to apply the force necessary to compress the steel back to the size it was before heating.  We can calculate the expansion, and the expansion due to forces, just as you suggest.  You can look up some properties of metals, and you will find a yield strength, an ultimate strength, a Young's Modulus and a coefficient of thermal expansion.  You may also find Poison's Ratio.  Let's look at each in turn.  The yield strength is the stress limit beyond which there will be some plastic definition.  The ultimate strength is the stress beyond which the material can be expected to break.  If you take a piece of steel strip, say 2 mm thigh by 25 mm wide and gently bend it with your fingers.  If you bend it just a little, it will spring back straight.  You may be able to bend it a little more and still have it spring back.  But there comes a point where it no longer springs back all the way to straight.  Without going into the stress analysis, in bending, the stress is not uniform as it might be if you just tried to stretch the steel lengthwise, but the point where the strip no longer springs back to straight, is the point where the highest stressed areas undergoes some plastic deformation, or permanent deformation.

Young's modulus is the property that relates the load to the deformation in the linear or elastic range.  This is the one you use to calculate the stretching or compression due to the pressure load, or other mechanical loads.  Nearly all mechanical design aims to keep the stresses within the electric limit.  Now there is considerable variation in the strength of even the best materials.  And it is quite difficult to apply a load so it is totally uniform.  In practice, quite generous safety factors are normally applied, so that there is minimal chance of the elastic limit being exceeded.

The coefficient of thermal expansion is the one you use to calculate how much the material expands as it is heated.  (Or contracts when it is cooled.). The figure for steel, from memory, i.e. not very reliable, is about 6.3 x 10^-6 in/in per degree Fahrenheit.  Funny tricks the memory plays.  But you will recognise that in/in is dimensionless, just a reminder really, so the units are really just per degree F.  But the expansion is measured in millionths of an inch in each inch of length of the component for each degree temperature change. My access to books and technology is limited at the moment, I don't have the right book with me, so apologies for being approximate.  The figures will vary for other materials.  I think aluminium is much more, brass and other copper alloys in between. 

Thermal expansion is interesting.  Things expand from a geometrical centre in all directions, whether the material is there or not.  So an engine cylinder expands just as much as a solid block.  The bore expands, not contracts.  So if the piston is the same material, and the same temperature, the clearance will also expand in proportion.  And this expansion, so long as the temperature is uniform, causes no stress in the material.  Well if not from the expansion, where do thermal stresses come from?  There are two causes for thermal stresses.  First if the temperature is not uniform.  If the temperature is not uniform, the expansion is different in different parts, but they are joined together.  So what ever stress is necessary to deform the parts so they are still joined, will appear.  Either that, or something will break.  If heating is slow, and particularly if things are insulated, the temperature can be kept uniform within reasonable limits.

The second source of thermal stresses is when different materials are in the same component.  If you fabricate a cylinder from say a brass tube and attached flanges made from a material with a lower coefficient of expansion, the flanges will tend to compress the ends of the cylinder to a slightly smaller diameter.  Of course with Paul's very small cylinders, the magnitude of this difference might be much smaller than reasonable construction tolerances, but it is worth knowing what is happening.  So the whole fabrication is best made from the one material.  Of course you may wonder about the silver solder.  When everything cools down, the solder may experience some local stresses.  Similar to the distortion of an improperly supported welded joint when it cools.  But even if there is a little plastic deformation on cooling, this is not a disaster, the stress is relieved by the plastic deformation.  Disaster is only when things are so severe that the joint cracks.  There are many build logs on this forum that illustrate that a well made silver soldered fabrication is normally quite sound.  So no reason to avoid fabricated components.

Willy, your second question was about how to support the cylinder on the frame to avoid expansion issues.  We are all familiar with the well known vertical engines.  The cylinder is supported on top of the cross head guide.  The cylinder expands upwards from the mounting face.  The close contact of the cylinder with the mounting flange means they are practically the same temperature, so both the cylinder and the head are expanding together.  If the cylinder and the cross head guide are both cast iron, they even expand the same amount.  The cross head guide and its mounting bolts are all stretched vertically by the rod load forces, but as we have observed they are usually made strong enough to resist the forces.

When the cylinder is mounted without the symmetry of the vertical engine, for example my mill engine which you can see in the engine gallery, the cylinder is mounted on its side on a steel base plate.  The centre line of the cylinder is well above the plate, as are the main bearings.  So the forces on the cylinder and main bearings are not in line with the base plate.  This of course results in some bending forces on the base plate.  Now you can see that the base plate is quite solid and easily resists the bending forces from this small engine.  There was a recent excellent build log by one of our members is Germany, my apologies to him that I can't remember his name for the moment, but look for the In Line Engine.  The cylinder is mounted on its centre line, and the symmetrical frame on each side properly balances all the loads.  It also has an interesting valve linkage and governor, but I believe the "In Line" designation refers mainly to the main rod load being in line with the centreline of the symmetrical frame.  It was beautiful workmanship.

Paul's locomotive had cylinders mounted I think between the locomotive frames.  Each frame is relatively flexible alone, but the cross bracing between frames is intended to stiffen the frames and the symmetrical nature of the frame and cylinder block configuration properly resists the bending loads as well as the tension.

I think that leaves the issue of expansion of the cylinder where it is attached to a frame on the side.  It is time to defer that one until tomorrow.

Looking forward to seeing those cooling curves Willy.  You look well equipped so far.  Degree F does give you smaller steps which may help give smoother curves.  Remember to control or at least record all the significant variables, ambient temperature, cup design, mass of tea.  May be better to do it with hot or boiling water instead of sacrificing a perfectly good cup of tea, though it is in a good cause.  The i Pad timer is very good for such experiments, it will record several times requiring only one touch for each time, so by a single touch say every 5 degrees, you will have an accurately recorded time to use in your graph.  You may want to make a thermowell by folding a drinking straw, and inserting the thermocouple in one side instead of placing it directly in your tea.  A K type thermocouple is a standard device for which the metals of the two wires are defined by standards, as is the voltage for each temperature.  Fortunately the calculation from voltage to temperature is included internally in most multimeters these days.  It should not need calibration, but it never hurts to check it at 32 F and 212 F.  Easier said than done though.  The boiling temperature is affected by atmospheric pressure, so not easy to achieve the 212,  the ice point is a bit easier as in principal you only need ice, and water in an open vessel, hence also water vapour to give 0.01 C = 32.018 F, near enough to 32, but do have plenty of ice.

Thanks everyone for following

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #186 on: July 30, 2017, 05:14:56 PM »
Hi, I have done a preliminary graph and it is quite interesting asa there is a quick drop in temp, then it stays the same for a few mins then falls gradually 1 degree a minuet. it looks like the heat rushes into the cup and spoons then finds it has nowhere else to go so comes back and thinks about it then decides to make the best of a bad job and gives off the rest of the heat in a begrudgingly manner ??!!! Are there technical terms for some of these adjectives ?!!. What i did was to pour the coffee this time in to the cup with the the teaspoons and temp node already in it. In the cafe the temp of the water to make tea is actually 80 degrees rather than 100 c Next i will try it with equal dimensions bars of copper, brass, bronze, aluminium and SS. and see how this performs. In all my text books there is no mention at all of differential expansion problems, and looking at a huge Triple expansion engine that would be in the Titanic, one wonders how much the engine would grow !!?

Offline paul gough

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Re: Talking Thermodynamics
« Reply #187 on: July 30, 2017, 11:30:21 PM »
Thanks again for the comprehensive reply on the cylinders, and the extension to 'expansion' prompted by Willys questions, thanks Wily.  I was particularly taken by your sentence, "Things expand from a geometrical centre in all directions, whether the material is there or not." Conjuring an image of a cylinder in my mind as I read this extraordinarily succinct and illuminating sentence led to an immediate grasp of the phenomena. A situation where previously my intellectual myopia had glossed over the origin, geometrical centre, because I was only thinking in terms of the bore getting bigger or the cylinder body growing as more or less separate things. Oh, if only all engineering explanations were so eloquent!!!

I have a fantastical question that keeps penetrating my mind and which I can't reconcile because I am confounded by internal energy and the spectre of irreversibility/reversibility etc. The Scenario: (1) A normally working cylinder and piston arrangement, but the cylinder body, including all covers, piston and rod etc. are somehow heated to and maintained at the temperature of the inlet steam, (say 150C); (2) All these elements heated to a high degree and maintained, (say 5x inlet temp).  (3) Would case (1) be somewhat equivalent to all the components being made of a perfect insulating material? Thus, are there any substantial changes to how our steam (heat) engine works, (or doesn't work), with these three situations???? Many thanks for your patience and effort in dealing with my confusions. Regards Paul Gough.   

Offline MJM460

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Re: Talking Thermodynamics
« Reply #188 on: July 31, 2017, 01:13:55 PM »
Willy's tea cooling experiment.

I was going to talk about thermal expansion but I would first like to look at Willy's tea cooling experimental results.  Willy, your graph is very well done and gives a lot of information about what is going on.  Let's look at three distinct phases, first that quick initial drop, then the steady temperature then the continuing cooling.  Your explanation is not bad so let's look at the technicalities.  Then try and deduce what it means.

That initial quick cooling is due to the teaspoons absorbing heat as they absorb heat from the coffee.  Remember stainless steel has poor thermal conductivity so it is not instantaneous.  We would expect the temperature drop to be greater for additional teaspoons.  But we have some  complicating factors.  First, the cup will also absorb some heat from the coffee.  We can get a good idea of how much heat the cup absorbs by looking at the curve for zero teaspoons.  There is a gap you have not told us about, the coffee starts at 80 deg C, which is 176 deg F, but your graph starts at 150 F.  Is that perhaps due to some air cooling of the coffee on the way from the machine to the cup?  Then I notice the 3 spoon experiment started at a lower temperature.

We can analyse what is happening in this way.  We have three components in the experiment, the cup, the coffee and the teaspoons.  Each brings an initial quota of heat to the experiment.  We could use absolute zero for the starting temperature, but the properties are not exactly constant over the necessary temperature range.  It is easier and a bit more accurate to use 0 , F or C depending on which we are working with.  The initial quota of heat for each is calculated as
Mass x specific heat x temperature - ref temperature, which we have nominated as zero, you can now see why.  When the coffee hits the cup and teaspoons, all three end up at the same temperature.  So we need only to calculate a temperature, t at which all three have the same temperature, but the total heat is still equal to the sum of the three initial quotas.  So you can see we need to know the initial temperature of the cup, the teaspoons and the hot water.  We don't know much about the cup, and it will end up hotter on the inside against the coffee, than the outside which is being cooled by the air.  However the zero teaspoons experiment probably tells us how much heat the cup absorbs, if we know it's initial temperature.

The initial starting point is probably not very important if we have the first temperature reading, and note that this is probably not at zero time for the complete curve.  However to keep the teaspoons and cup effect separate, it may be better to let the cup cool the coffee, then add the teaspoons as soon as the initial drop is complete, say as soon as you have two consecutive readings that show the levelling off, so you see the quick drop when the spoons are added separately from the effect of the cup.

Then we have that roughly constant temperature period.  We have to be careful in our explanation of this phase to be sure that we do not violate known laws of thermodynamics, in particular that heat cannot flow from one item at one temperature to any other place which is at a higher temperature.  Heat can only flow from hot to cold.  However, plunging the cold teaspoons into a hot cup of coffee is not equilibrium at every tiny increment through the change.  It is not a reversible process, but it also does not happen slowly is a series of tiny equilibrium steps.  It is likely that the coffee in the cup is initially over cooled in the immediate vicinity of the spoons, leaving it a bit cooler than the coffee in the more distant parts of the cup.  Then, the heat flows from the warmer coffee to the cooler until it is all at the same temperature as convection currents redistribute the heat in the cup.  The temperature measurement may also be affected by the location of the thermocouple, relative to the teaspoons.  It really requires a bit more experimentation.  The initial purpose of the teaspoons was to cool the coffee to drinking temperature, in which case we might try stirring the coffee to maximise heat transfer coefficients to the cup and air at the surface and keep the temperature more uniform.  Worth a try.  May have to try a few times at home with the kettle, to save some coffee cost, while determining the optimum experimental method.

Now the third stage.  Let's just look at the two that start at the same temperature.  It certainly looks linear, but if you continued until almost at air temperature, (which we should record), it would show a curve, as the heat loss slows due to the decreasing temperature difference.  You can see the curve in the zero teaspoons curve.  But notice that the curves with and without teaspoons cross over after a while.  Can we explain that?

Let me make a suggestion.  When the teaspoons are plunged into the coffee, the heat is not lost, some of it is just stored in the spoons.  It is not lost until it goes to the air either through the walls of the cup, or through evaporation at the surface.  But the lower temperature due to the spoons reduces the temperature difference driving the cooling, so the coffee cools slower, but the same total amount of heat has eventually to be transferred to the air.  The cup with no spoons initially cools faster so the heat is actually lost to the air.  So when the slow one gets down to the point where it is the same temperature as the one with the spoons, the two at that moment cool at the same rate, but the one with the spoons still has more heat remaining in the coffee plus spoons so it's temperature drops slower.  So the spoons not only initially cool the drink to drinking temperature more quickly, they actually keep it near that temperature for longer.  Bonus points to anyone who saw that coming, I certainly did not.  It also casts some doubt on my text book which suggested that the spoons added cooling surface like fins to help cool it faster.  Either it's a very small effect, or the conductivity of the stainless steel puts the handles in that category where fins actually are counterproductive.

I think everyone will now be waiting for the next experimental results.

Thank you Paul for your kind words, I am glad that my explanation was helpful.  I hope that others have found it equally helpful.  Many people are confused by this point, but one time I had to analyse a large vertical pressure vessel with heavy parts suspended inside from a nozzle in the middle of the top head.  It was during my work on this that the penny dropped. 

Enough for today, current intention is to continue on control of thermal expansion and the cylinder heating questions tomorrow.

Thanks to everyone following,

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #189 on: August 01, 2017, 11:50:06 AM »
Thanks for this synopsis and i shall rethink the next experiments as there are so many variables to consider I may start with boiling water at home rather than  coffee in the cafe as i was getting some funny looks !! Also trying to get the waitresses to come over strait away with the coffee was a bit difficult . ! was going to transpose the 3 teaspoon graph onto the starting point for the others but that would have made the graph a bit over loaded!! so , we shall do some more work over more controlled conditions.........

Offline MJM460

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Re: Talking Thermodynamics
« Reply #190 on: August 01, 2017, 01:16:39 PM »
Thermal expansion issues.

Hi Willy, We are obviously thinking about this at about exactly the same time.  I should have mentioned yesterday that the end temperature would not be much affected by the order you do things in those first few seconds, however by carefully doing things in a suitable order, you can see the separate effects, and thus isolate the effect of the teaspoons from the other things such as air cooling during pouring, and heating the cup.  Of course I didn't think of the time for the waitress to deliver.  Boiling water at home allows you to control much more of this.  By the way, if you have some silver plated brass teaspoons, these have better conductivity than stainless steel so the handles might make more effective fins, would be interesting to see.  The specific heat of brass is 385 J/kg.C compared with 461 for stainless steel so you would need about 20% more mass of spoons, about 6 brass spoons compared with 5 SS ones of the same mass.  Though you could stay with the same number of spoons and see a smaller initial temperature drop.

Continuing our discussion of thermal expansion issues, let's look at a few examples.  Willy you mentioned the engines on the Titanic.

Now I have no idea of what size these engines are, or what temperature they operate at, so I will make a few wild guesses to use for calculating representative numbers.  Thermal expansion is fully proportional to the length being heated, or cooled, so if the real engines were double the height I have guessed, then the expansion will be double.  Perhaps someone will be able to join in with the actual engine dimensions.  Let's assume an engine 6 metres high from the crankshaft centre line to the top cylinder head, consisting of a cylinder 1 metre high and support structure 5 m high.  In the typical model marine engine the cylinder is mounted on a table at the top of columns.  A larger ship might have a more substantial support incorporating the cross head guide.  Further let's assume the engine was built at 15 degrees C and the steam inlet temperature is say 250 deg C.

Thermal expansion is determined by the length of the component, the temperature change and the coefficient of thermal expansion of the material.  If the engines were made of cast iron, the coefficient of thermal expansion is 13.5 by 10^-6/deg C (or 7.5 by 10^-6/deg F).

Let's assume the cylinder is well insulated and operates at the steam inlet temperature of 250 deg C.  As I have previously mentioned, steam cools during expansion so the average temperature would be a little lower, but then the steam inlet temperature may be a bit higher.  These assumptions contribute to inaccuracy, but the calculation is still useful.

The cylinder then expands by d = 13.5 x 10^-6 x 1 x (250-15) = 0.003 m or 3 mm.  This may not seem like much on an engine of that size, however the clearance between the piston and the cylinder head at top dead centre may not be much larger than that.

If we look at the cylinder support, the metal at the top is in close contact with the cylinder so let's assume 250 degrees C.  However at the bottom end, at crankshaft level, it is probably nearer engine room temperature, say 40 deg C.  We can assume that thermal expansion is linear so the expansion can be calculated by assuming it is all at the average temperature, (250+ 40)/2 = 145.

Now calculate the expansion d = 13.5 x 10^-6 x 5 x (145-15) = 0.0088 m or nearly 9 mm.

So we can estimate that the distance between the crankshaft and the top cylinder head is 9+3= 12 mm.  You can see it would be pretty small on a model engine.  It is important to understand that, so long as we allow that expansion to go unrestrained, there is no force or stress involved.  It would take very high forces to restrain the engine to its original dimensions.

So far I have assumed that the whole cylinder block is at one temperature, the steam inlet temperature.  However, the question was about a triple expansion engine, and the temperature for the the low pressure cylinder is quite different from the high pressure cylinder.

For the lp cylinder, assuming a condensing engine, the cylinder temperature might be nearer 40 deg C.  The temperature difference is then 40-15= 25 deg C, instead of 250-15=235 in the high pressure cylinder.  With a temperature difference of approximately 1/10, so the expansion of the cylinder would be 0.3 mm instead of 3 mm.  More importantly, the stand at the lp end has a thermal expansion very close to zero, compared with 9mm at the hp end.

Even with the necessary approximations, I think you can see the problem.  If the three cylinders are machined in one casting, there will be significant internal stresses in the casting as one end expands under the inlet steam temperature, while the other end undergoes minimal expansion at the lower operating temperature.

Remember at the start of the discussion on thermal expansion I said we cannot control this expansion, we can only learn to live with it.  I suspect that in this case, the engineer might set up the engine cold with the lp end a little high, so that when the engine is hot, both ends are at the same height.  He would then have very careful heat up procedures to avoid any problems during warm up.  Now we have a few marine engineers on the forum, perhaps they could chip in and comment on the thermal expansion issues they see, and what they actually do.  I don't have any practical experience with real ship engines so would appreciate any help that is offered.

There is one area that we can control with regard to the thermal expansion.  I mentioned earlier that materials expand in all directions away from a geometric centre.  However nothing says that geometric centre has to be stationary.  We can choose which part of the engine is fixed stationary, and let the expansion go from there.  The geometric centre moves away from that fixed point, and the rest of the material expands away from the altered position of the geometric centre.  On a ship, the crankshaft would be fixed in line with the propellor shaft, and the engine allowed to grow upwards from there.  The remaining problem to be solved is that the piping to the engine must be designed to be flexible enough to allow for the movement of the cylinder flanges.

I hope this simple approach to expansion sheds some light on the issue.  These days with finite element methods we can do a much more exact analysis of exactly what happens, however that might be considered a bit over the top for our model building purposes.

We should have a quick look at how expansion effects a horizontal mill engine before leaving this topic.  Also a few questions from earlier posts still to be tidied up, then back to condensers.

Thanks for following along.

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

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #191 on: August 01, 2017, 03:21:55 PM »
Having looked at Utube ,the engine are described as 4 cylinder triple expansion engines ??. Also all the cylinders are separate !! so they knew about thermal expansion. I do not know what the other cylinder did in the engine ...any ideas? Will look further into this and here a few pics off the web

Offline Dan Rowe

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Re: Talking Thermodynamics
« Reply #192 on: August 01, 2017, 03:54:06 PM »
Willy, it was common to use 2 cylinders for the low pressure expansion to keep the cylinders smaller. If you notice the violet line it is the exhaust and it is connected to both LP cylinders on the ends.

Dan
ShaylocoDan

Offline Ye-Ole Steam Dude

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Re: Talking Thermodynamics
« Reply #193 on: August 01, 2017, 05:03:32 PM »
Having looked at Utube ,the engine are described as 4 cylinder triple expansion engines ??. Also all the cylinders are separate !! so they knew about thermal expansion. I do not know what the other cylinder did in the engine ...any ideas? Will look further into this and here a few pics off the web

It appears looking at the picture from right to left, the fourth cylinder somehow helped “balance” out the crankshaft. Again looking right to left, cylinder #1 is at 0-degrees, cylinder #2 is in retard at 120-degrees ( assuming clockwise rotation), cylinder #3 is at 0-degrees, and cylinder #4 is in retard by 240-degrees. Just my observation and would like to find out.

Offline Maryak

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Re: Talking Thermodynamics
« Reply #194 on: August 01, 2017, 11:23:21 PM »
Triple Expansion Steam Engines

1. Cylinder Volumes:
HP = 1.0
IP = 2.6
LP = 7.0

To keep the LP Cylinder a manageable diameter it was split into 2 cylinders at 3.5 x HP volume giving a 4 cylinder triple expansion engine normally arranged from front to back LP,HP,IP,LP.

With this arrangement balance was achieved by setting the cranks at:
Between Forward LP and HP 1660
Between Forward LP and IP 2700
Between Forward and Rear LPs 700
In addition suitable counterweights were added to the crankshaft.

With Titanic and Olympus, not shown is a turbine which utilised the LP exhaust to drive the centre propeller. For manoeuvering the exhaust was switched over from this turbine and sent directly to the condenser. This made emergency reversing/stopping difficult as until this exhaust was removed, the turbine continued to move the centre propeller ahead. Transfer was accomplished by some big hand operated valves!

HTH
Regards
Bob
« Last Edit: August 01, 2017, 11:37:57 PM by Maryak »
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