Steam Engine

Hello,
I am a mechanical engineer and haven't touched anything that has to do in thermodynamics for 15 years (gosh I just realized how long ago I graduated).
I am working on a steam engine and its been a bit rusty to get back into the whole subject. One Thing that I am not able to figure out is how to figure out the temperature and pressure at the outlet side of the piston.

Can anyone help out?

There are four events that happen in a typical double-acting steam engine cycle, and the pressure varies on both sides of the piston.

Looking at the graph (called a card; top card for one end of the cylinder, and a separate bottom card for the opposite end of the cylinder), you can determine the pressure on the face of the piston at any given moment in the cycle, but it is a variable thing.

The valve actually closes before the piston finishes its stroke, called the "compression" point, so that the cylinder pressure rises, and a cushion is provided at the end of stroke.

The efficiency of a steam engine is generally controlled by varying the cutoff point (point at which the steam entering the cylinder is cut off). An early cutoff gives a more efficient operation, assuming that the required power can still be produced.
Steam locomotives use a variable cutoff, so that they can produce full power using a late cutoff when starting a train, or when traversing up steep grades, and then an earlier cutoff when full power is not required to move the train.

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Thank you @GreenTwin for this chart. That is very extensive.

I am looking at the Doble steam engine used on the E-20. From my understanding, it uses pairs of single acting cylinders. One that is high pressure and one that is low pressure. From what I found is that is uses 51.7bar steam pressure at the inlet at 400C. Would the same Top card apply?

From the numbers that I found I got the following calculated:
HP=High Pressure; LP=Low Pressure, * indicate I picked that value, otherwise its calculated, and they are subject to change
Diameter of HP piston=70 mm*
Stroke=60 mm*
Area of HP piston=0.004 m2
Area above the piston 25%* of the total volume (Total volume will be stroke volume + area above piston)
F= P x A =19896.49 N
Volume before expansion= 0.000115 m3
Volume after expansion= 0.000577 m3

Here I am looking to see what would the pressure and temperature be so I would know what the area of the LP piston be to maintain same force as the HP piston, also how much heat I need to reintroduce to the steam to get it back to the same temperature of 400C

Which I will calculate using the Q=m x c x (dT)

looking for advice on the soundness of my approach

Looking through my old Doble literature, I can't find the info I was looking for, but I did find some into.

It looks like Doble made two and four cylinder engines.
I recall that the Doble brothers were I think M.I.T. engineers, and in my opinion way ahead of their time.
There engines seems ultra-sophisticated for the time, and even for modern times.

While I see a two cylinder single-expansion, double-acting Doble, I don't see any Doble engine that was single-acting.

The Doble 4-cylinder was double-expansion, double-acting, cross compound.
Some of the Doble engines were Uniflow, which is an efficient design that seems to have gained popularity later in the steam era.

If you have a high and low pressure cylinder, then the engine is a compound type.

There was a V-twin steam airplane engine that I recall was single-acting.




The terminology can get a bit confusing.
There was a huge variety of steam engine styles, and valvegear styles.

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I can't really comment on your calculations; I am not that smart.

I do know that the compound steam engines generally used significantly higher steam pressure, and often with superheat.

As I understand it, the intent with compound designs is to balance the forces on the high and low pressure cylinders.
The exhaust of the high pressure cylinder is fed to the low pressure cylinder, and so the calcs to balance the forces takes hp and lp piston sizes and pressure drops into account.

That is about all I know.

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I have seen a book where the take cards for the high and low pressure cylinders, and they can show that the power is equal on both.

I think the power is the sum of the area under the curve.

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ejrego said:

Thank you @GreenTwin for this chart. That is very extensive.

I am looking at the Doble steam engine used on the E-20. From my understanding, it uses pairs of single acting cylinders. One that is high pressure and one that is low pressure. From what I found is that is uses 51.7bar steam pressure at the inlet at 400C. Would the same Top card apply?

From the numbers that I found I got the following calculated:
HP=High Pressure; LP=Low Pressure, * indicate I picked that value, otherwise its calculated, and they are subject to change
Diameter of HP piston=70 mm*
Stroke=60 mm*
Area of HP piston=0.004 m2
Area above the piston 25%* of the total volume (Total volume will be stroke volume + area above piston)
F= P x A =19896.49 N
Volume before expansion= 0.000115 m3
Volume after expansion= 0.000577 m3

Here I am looking to see what would the pressure and temperature be so I would know what the area of the LP piston be to maintain same force as the HP piston, also how much heat I need to reintroduce to the steam to get it back to the same temperature of 400C

Which I will calculate using the Q=m x c x (dT)

looking for advice on the soundness of my approach

Click to expand...

Usually the flow from the high pressure cylinder is dropped into a second cylinder an the steam is expanded at lower pressure. It does not flow back to a heat source like a reheat turbine. You would have to know the pressures to even out the force. What is important is the mean effective pressure you will develop when the steam is put to the low pressure cylinder for it is that number that determines the forces generated. So basically its a thermodynamic problem to reach the state properties for the lower pressure cylinder. But for starters the mass flow rate through each cylinder will be the same but the work extracted will depend on piston areas and the mean effective pressures. It would be complicated to reheat the steam from the first cylinder.

ejrego said:

Hello,
I am a mechanical engineer and haven't touched anything that has to do in thermodynamics for 15 years (gosh I just realized how long ago I graduated).
I am working on a steam engine and its been a bit rusty to get back into the whole subject. One Thing that I am not able to figure out is how to figure out the temperature and pressure at the outlet side of the piston.

Can anyone help out?

Click to expand...

so from high school you should remember P x V = n x r x T, the relationship that says Pressure and Volume are inversely proportional to Temperature (for a fixed quantity of gas, EG steam).

you do know the volume change of your cylinder, but that's one equation in three unknowns so is useless by itself, sadly they don't teach the other equations until you take a course in thermodynamics specifically, which is
P x V^gamma = const (for a fixed quantity of gas/steam)
the exponent gamma depends on the type of gas, 1.4 for diatomic molecules like N2 and O2 which comprise about 99% of air, but steam, H2O, is triatomic so use 1.333 for steam,
knowing that equation you can then derive
PR = TR^(gamma / gamma-1), VR = PR^(-1 / gamma), TR = PR^(gamma-1 / gamma)
PR = VR^(-gamma), VR = TR^(1 / 1-gamma), TR = VR^(1-gamma)
these are ratios equations, PR = Pressure Ratio (after vs before)

and the all important (also not taught until thermo class) energy equation
E = T[in] x Cp x (1 - PR^(1-gamma / gamma))
Cp = coefficient of heat at constant pressure for the gas, which is fairly
constant for air but varies a bit for steam depending on its temp
Cp for air is about 1000 J/kG/K, for steam is about 2000 J/kG/K
(MKS metric units, Joules, kiloGrams, degrees Kelvin)
and its inverse
PR = ( E / Cp / T[in] - 1 ) ^ (gamma/(gamma-1))

so now in theory you have all the equations required to solve the problem, except...

...you don't really know how much steam actually got into the cylinder because of valve timing events

you might want to start by assuming that at cut-off the cylinder is at boiler pressure and temperature (it will actually be less), and then for your VR (volume ratio) assume it all exhausts as soon as the exhaust port starts to open (again, not true), and you'll find you haven't expanded it down to atmospheric pressure (hence the "puff" at the exhaust) and it will still be quite hot (wasted energy).


happy computing !
Pete.

Thank you very much guys, that has been very helpful. Especially the formula provided by @peterl95124. I was able to get at least a preliminary design of the pistons required to generate the forces.

For the next step, is there any tips and recommendations when it comes to designing the piping and pistons? Especially to keep them from pitting or any other issues that you might know about.

The high pressure pistons were often domed shape one piece, and the low pressure were often built-up from several pieces with a spider in the center.

If a steam engine is used reqularly with an oiler, corrosion should not be a problem.

If a steam engine is used occasionally, you need to get WD40 into it to displace the water/moisture.

Mild steel is bad about corroding inside of a steam engine.
Many use stainless piston rods, and perhaps a cast iron piston.
Cast iron has a very slow corrosion rate.

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@GreenTwin Thank you for your advice. I was thinking of looking into using some composite material for the pistons. I will test and simulate different options. If it doesn't work my second choice was cast iron.

Do you have any advice on the bearing material between the crankshaft and connecting rod? I am planning on using a brass sleeve bearing or another type of composite plastic, something that has low wear and tear and self lubricating. Of course I will be testing the heck out of the plastic before saying for sure which direction I need to go.

I see a lot of brass/bronze used on various parts, since it has good strength and corrosion resistance.

Bearing bronze is a very good material for bearings, but I see brass used too, and while brass does not wear as well as bearing bronze, it seems to be more readily available, and seems to be ok as far as wear in many model applications.

Crankshafts are often built up steel.
I use precision ground steel, such as 1045 ground and polished rod.

For crankshafts cut from a single piece of solid steel, people often use stressproof 1144 steel, so that it does not deflect after machining, since its internal stresses have been relieved.

I am not into plastic for any use on an engine, but to each their own, and it if that works for your particular engine application, then more power to you.
Some folks 3D print entire engines in plastic, and then assemble and run them, with no load of course, and so there is that side of the hobby.

I use a lot of cast iron because it wears well against steel and other metals, and wears well against itself.
Gray iron is easy to machine (discounting some poorly cast parts that were cooled too quickly with hard spots), does not tend to grab the tool bit like I have experienced with brass, and it does not corrode easily as far as anything beyond superficial surface corrosion.

Hope this helps.

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Is there a reason why the high pressure pistons were domed?

Looking through prints in the old books, there is no consistency in piston design, but the one-piece domed design does seem to be commonly used on some engines.

Perhaps used on high power marine engines such as Naval engines to keep the weight and reciprocating mass to a minimum.

The domed piston is a more complex design from the standpoint that the heads must fit the shape of the piston.
The domed one-piece piston by itself is a pretty simple design.

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That is a nice collection of cross sections. Were those domed pistons made from cast iron? My guess would have been that this is related to pattern removal and beeing able to cast concentric round pieces easy.

I think much of the old steam engines (cylinders, etc) were cast in gray iron.

I am not sure about things like one-piece pistons, crankshafts, connecting rods, etc.
They made steel earlier than I thought (according to one source), but I am not sure when it came into normal production for engine work.

Malleable iron came into use at some point, but not sure if it was used in steam engines.

The flat top/bottom pistons I suspect were gray iron, and they had a spider cast inside, to keep the piston as light as possible.

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Those seem a little bit too complicated for today's manufacturing capabilities. I think some casting and machining afterwards can help reduce the number of pieces. I was running some FEA on aluminum and they seem to be doing good

The conical shape is stronger than flat... so it is simply to reduce mass for the same strength/ stiffness.
I'm surprised anyone may consider the shape "too complicated for today's manufacturing capabilities". More a case of keeping it simple when the excess material isn't an issue... Very few large steam engines are manufactured today, so maybe I misunderstand your comment?

K2

Sorry I worded that wrong. What I meant that with today's capabilities, we can make a simpler design.

No problem. I guessed you had meant something a bit different from the words...
But I'm also sure that we could make the whole engine much higher performance and more economical is we used all the finite element analyses, fluid mechanics modelling tools, etc. that are bread and butter in today's design office.
And we could make any shape that is the optimum for the constraints and advantages from the modelling.
Pistons I was working with started cracking towards the hub when I increased performance from the air motor I worked on in the 1980s. One guy had the first finite element modelling software (1985) on a PC - The first in the company! He used it in the piston section as a cantilever beam, and determined the previous design of lightened pistons was too thin for stress concentrations near the hub, so we made a curved face one side + flat the other to fit the end face with minimum cavity so we put material in where it was needed and took it out where we could and reduced the mass by a few %, yet increased strength and durability by factors of 1000 for fatigue stresses.
So I have "been there, done that".
K2