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Random Thoughts on Steam Injectors

A Repository for my Ideas on Steam Injector Theory and Design

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julian atkins18/11/2015 22:33:20
1254 forum posts
353 photos

hi Andrew,

what is the point of going off on a flight of fancy when all the data and design details are already known and well established?

there is no point trying to re-invent the wheel.

you wont arrive at anything better than what has been known for 100 years in fullsize, and 75 years in miniature.

all you will do is to say 'hey, ive done this all myself, and this guy in 1905 at Gresham and Craven did the same, or this guy at Davies and Metcalfe did the same in 1906'.

have a look at the following. it takes a while to download.




Muzzer18/11/2015 22:59:16
2904 forum posts
448 photos

I guess that's because Andrew is an engineer rather than a mechanic and likes to understand the subject matter before designing himself what he is going to make.

Many of the scale injectors must have questionable parentage - simply scaling down the full size parts doesn't generally work, which may explain why some model injectors seem to work while others don't (dimensional analysis, anyone?).

Unless you know something was actually designed rather than thrown at the wall until it seemed to stick, you may be better to design it yourself, assuming you have the brainpower to do so - a PhD in engineering from Cambridge in Andrew's case.

I wonder when someone last actually designed an injector - and are they still alive? I'm looking forward to the next instalment and hopefully seeing the end result. At least Andrew is publicly putting his c0ck on the block here - very sporting!


julian atkins18/11/2015 23:19:23
1254 forum posts
353 photos


i was very privileged to have known and taught how to make injectors by Arthur Grimmett who made well over 3,000 for Reeves and Kennions, plus i knew Gordon Chiverton who made all of the injectors for Don Young and others subsequently. all were 100% reliable and the top end of the market. i wont comment on inferior examples. i make my own, and all my locos have only 2 injectors fitted and no axle pump or hand pump. i often get sent problem injectors to sort out. some of the cheaper products are atrocious.

the design parameters have been very well established for very many years. that some poor quality commercial products dont come up to scratch is self evident on examination and test. however that does not detract from the fundamental principles which are well established and tried and tested. if Andrew wishes to side step all of this and spend hours and hours on a pointless endeavour that is entirely up to him of course.




Edited By JasonB on 19/11/2015 07:35:41

Gary Wooding19/11/2015 12:14:17
983 forum posts
254 photos
Posted by Andrew Johnston on 18/11/2015 11:42:55:

The engine is double acting, so steam fills the swept volume twice per revolution, so:

9.423 x 2 = 18.85 in³

Thanks Andrew, I missed the fact that it was double acting, so I ended up with .093 m³ and couldn't see where I'd gone wrong.

Andrew Johnston19/11/2015 12:30:56
6601 forum posts
701 photos
Posted by Gary Wooding on 19/11/2015 12:14:17:

Thanks Andrew, I missed the fact that it was double acting, so I ended up with .093 m³ and couldn't see where I'd gone wrong.

So did I the first time round the loop. embarrassed


Andrew Johnston20/11/2015 12:13:03
6601 forum posts
701 photos

A further thought; it seems to be generally accepted in the literature that around 10-15% of the internal energy of the incoming steam is lost as heat due to friction with the sidewalls of the nozzle. So presumably there is an incentive to keep the nozzle as short as possible, and also ensure that the surface finish is good. Presumably the heat lost is dissipated into the wider world? So what would happen if we made the nozzle from a material (plastic for instance) that has poor heat conductivity? Would that result in less of the heat generated by friction being lost?


jason udall20/11/2015 12:23:58
2031 forum posts
41 photos
And there you have it.
" why re invent the wheel"...
Materials change.
Processing changes...
THE solution is not always the only solution and may not be the best with availability of materials/process.
Neil Wyatt20/11/2015 14:59:18
19033 forum posts
734 photos
80 articles

> Would that result in less of the heat generated by friction being lost?

You might be up against entropy - an injector without heat losses would be a perpetual motion machine (as all you would need to do is raise the feedwater to boiler temperature and supply the tiny amount of energy to move the water from inside the boiler to inside). The heat being lost may help ensure all the steam is condensed by the water. On the other hand, it may mean you need less steam.


I remember thread failing to ex-plain injectors in simple terms. My interpretation is now that as the volume of steam is reduced as the boiler fills it gives up its latent heat of evaporation and this is where the energy to run the injector comes from.

Andrew Johnston20/11/2015 15:54:20
6601 forum posts
701 photos

I didn't explain that very well. What I should have said is heat lost to the outside world. In theory the expansion through a nozzle is adiabatic, so no heat is lost to, or gained from, the outside world. This also implies that the expansion is isentropic, ie, the entropy doesn't change. However, the fact that the expansion is adiabatic doesn't imply that heat can't be lost within the system. As I understand it the enthalpy of the steam decreases, and it is that decrease that provides the kinetic energy of the output steam. So one is simply converting one form of energy to another within a closed system.

On the other hand heating up of the injector due to friction from the steam flow results in that heat being lost, so the expansion is no longer adiabatic. It also means there is a loss of energy that could have been converted to kinetic energy.

So I suppose the question is: if the heat caused by friction is not conducted away through a metal steam cone is it available to the steam flow and can it be used to increase the kinetic energy of the output steam?


KWIL21/11/2015 14:03:34
3554 forum posts
70 photos

Just because Andrew Johnston wishes to put his thoughts down on paper (this Forum), there is no necessity whatsoever for anyone to to constantly refer to reinventing the wheel. There may well be others on this Forum who would be interested to watch the process being explained, rather than following some reference from the past. Perhaps they learn by example, rather than be lectured to.

Edited By KWIL on 21/11/2015 14:04:07

Andrew Johnston25/11/2015 23:30:11
6601 forum posts
701 photos

The numbers for the convergent part of the steam nozzle are falling into place, although I need to extract some wetness fractions for the steam at the throat so I can work out its enthalpy, the decrease in enthalpy and hence the speed of the steam at the throat. The divergent part of the nozzle requires a further look to understand it.

As a small diversion I've worked out what size steam pipe would be needed. Older professional text books give a value of 6000ft/min as being suitable for the general transport of steam via pipework. This ties in nicely with the 30m/s quoted by more modern text books. However, since are dealing with quite small pipes it seems prudent to halve this, so 15m/s for the speed of steam in the pipe to the injector.

We have previously calculated that we need 0.142kg/min of steam, assuming we have steam at 170psig. The mass of steam needed equates to 0.00237kg/sec and using the specific volume, from steam tables, of 0.1542m³/kg we get a volume of 3.65x10^-4m³ per second. We know that the volume of a cylinder is pi x r² x h. Since want a speed of 15m/s the value of h is 15. Dividing by 15 gives us an area of 2.43x10^-5m². From this we get a radius of 2.78x10^-3m. or in more practical units a diameter of 5.57mm.

A look at available tube sizes shows that 5/16" 22swg tubing has an internal diameter of 0.256" or 6.5mm. The use of Lamé's equations for stresses in thick walled tubing shows that the maximum hoop stress with steam at 170psig is 857psi. This is well below the yield stress of copper, taking into account a 20% reduction to allow for the steam temperature of 190ºC.


Andrew Johnston03/12/2015 21:23:54
6601 forum posts
701 photos

I've now understood enough of the mathematics to calculate the exit and throat diameters for the steam nozzle. The calculation is based on mass flow rates. We have already calculated the mass flow rate of steam we need for the water flow, vis 0.00237kg/sec. If that is the mass flow into the steam nozzle then it clearly has to be the same as the mass flow exiting the nozzle. So if we can calculate the exit velocity we can work out the exit area and thus the exit diameter.

First we need to set the input and output steam parameters. I've taken the input parameters to be nominally those of the boiler, ie, 170psig (12.734bar absolute) and assumed to be dry saturated steam. The input steam has a temperature of 190.7ºC and an enthalpy of 2786390J/kg. I found that the key to calculating the exit and throat diameters was specifying a sensible output steam pressure. This is something that seems to be barely touched upon in the ME literature. It is widely specified in the design of steam nozzles for steam turbines; where low values are used, 0.15bar absolute seems common. The specific volume of steam increases rapidly at very low pressures. Consquently this leads to large nozzle exit diameters; much larger than used in ME injector designs. For the traction engine I don't think it is necessary for the injector to be lifting and hence the output steam pressure shouldn't need to be below atmospheric. However, it seems prudent to aim for an output steam pressure a bit below atmospheric. I chose to do the calculations for 0.75bar and 0.5bar output pressure, both absolute.

I used the Mollier chart to estimate the dryness fraction of the output steam, assuming the expansion is isentropic, ie, a vertical line on the Mollier chart. In both cases I got a value of around 83%. I then used steam tables to calculate the following:

0.75bar absolute specific volume = 1.863m³/kg enthalpy = 2298080J/kg

0.5bar absolute specific volume = 2.690m³/kg enthalpy = 2253540J/kg

This gives a change of enthalpy as follows:

0.75bar absolute change of enthalpy = 488310J/kg

0.5bar absolute change of enthalpy = 532850J/kg

By equating the drop in enthalpy to the increase in kinetic energy we can show that the steam velocity at the output of the nozzle is 44.72 times the square root of the product of the change in enthalpy (in kJ/kg) and one minus the frictional loss. This gives the following output steam velocities, assuming a frictional loss of 0.12, or 12%:

0.75bar absolute output velocity = 927m/s

0.5bar absolute output velocity = 968m/s

Pretty darn fast!

This post is getting rather longer than I anticipated, so I'm going to take a tea break.


Andrew Johnston03/12/2015 22:37:31
6601 forum posts
701 photos

Tea break finished!

Now that we know the steam velocity at the exit of the nozzle, the specific volume of the steam and the mass flow, we can calculate the area and hence the nozzle exit diameter:

0.75bar absolute nozzle exit diameter = 2.46mm

0.5bar absolute nozzle exit diameter = 2.90mm

In a similar way we can calculate the throat diameter of the nozzle; although in this case the results are independent of the output steam pressure. There is no point in the steam pressure at the throat of the nozzle being below the critical pressure, as we will not get any advantage in terms of mass flow. So the pressure at the throat is taken as 0.58 times the input pressure, ie, 7.39bar absolute. From the Mollier chart we get a dryness fraction of 96%, and can then calculate the specific volume of 0.249m³/kg and an enthalpy of 2683300J/kg for the steam at the throat. In both cases the change in enthalpy is 103090J/Kg. The steam velocity at the throat is calculated in the same way as for the exit steam, except that the frictional losses are taken to be zero. For both cases we get a steam velocity of 454m/s; in rough terms a bit less the speed of sound in steam at the throat pressure. Similarly we can use the mass flow rate to calculate the throat area, and hence diameter to get 1.29mm. To summarise:

Output steam pressure = 0.75bar absolute nozzle exit diameter = 2.46mm nozzle throat diameter = 1.29mm

Output steam pressure = 0.5bar absolute nozzle exit diameter = 2.90mm nozzle throat diameter = 1.29mm

A further question arises as to the shape of the convergent and divergent parts of the steam nozzle. Here the ME words of wisdom and the professionals diverge (pun intended).

For the convergent part of the nozzle it doesn't really matter as long as the transitions are smooth and the recommendations in the professional literature is to keep it short. One publication mentions a length of 6mm; this for large nozzles with flow rates two orders of magnitude larger than my injector. The concept is discussed in the book by Crawford, and given the barest of mentions in the book by Brown. Both then go onto to use relatively shallow tapers. I plan to use a fairly short trumpet shaped convergent cone. Since the convegent part of the cone is short, and the steam velocity is subsonic, the frictional losses can be conveniently ignored.

For the divergent part of the nozzle again the actual angle isn't that important. Too shallow and the nozzle will be overly long with attendant frictional losses. Too steep and the steam may not be able to expand quickly enough, leading to turbulence. Values of around 10º included are discussed in the professional literature. This ties in well with practical ME injectors, where 9º seems to be a de facto value.

Given that the nozzle exit and throat diameters are calculated based on a series of idealised assumptions, and an estimate of frictional losses I don't think that they need to be particularly accurate in themselves.

Now that I have values for the nozzle exit and throat diameters the next phase of the investigation will look at the performance as the input pressure decreases to try and estimate the range over which the injector may work. I will also be looking at the kinetic energy and momentum available at various input pressures.


Andrew Johnston31/12/2015 11:42:16
6601 forum posts
701 photos

This post aims to tidy up a couple of loose ends as part of an end of year clear up.

The idea was mooted earlier that the injector steam cone could be made from a poor heat conductor in order to minimise the heat loss caused by friction. I was thinking in terms of a high temperature plastic, such as PEEK. In a PM exchange machinable ceramics, such as Macor, and more intriguingly sapphire, were suggested. Of course the wealthier modeller could use diamond. The problem with sapphire, and diamond, is that they are excellent conductors of heat. Both are used as substrates for specialised silicon integrated circuits to get the heat from the junction(s) to the outside world. So their use would be for the 'bling' factor only. A practical issue with PEEK and Macor would be getting the thin wall needed at the exit of the divergent part of the cone where the steam jet mixes with the incoming water.

So it looks like metal is still the best solution. It turns out that not all the enthalpy lost due to friction is completely lost. Some of it has the effect of drying the steam in the jet. This is advantageous as it means there is more steam, and less entrained water, in the output jet and hence the potential to input more water into the boiler.

I'm not surprised that no-one rose to the challenge of how you get a radio to operate through a 1" thick cast iron pipe. The answer of course is to use a low frequency, in this case 30Hz. At these frequencies we are clearly operating in the near field, so the radio is operating using magnetic induction rather than far field EM waves. It is a myth that EM waves do not pentrate metal, they do. The strength of the wave falls as 1/e for each distance known as the skin depth. The slin depth depends upon frequency and the conductivity of the metal, and at normal radio frequencies is very small. However, for 30Hz and cast iron, it is about 8mm. So for 1" of cast iron the signal strength drops by about 20, which is still usable.


Another JohnS31/12/2015 17:52:10
832 forum posts
56 photos

Posted by Andrew Johnston on 31/12/2015 11:42:16:

I'm not surprised that no-one rose to the challenge of how you get a radio to operate through a 1" thick cast iron pipe. The answer of course is to use a low frequency, in this case 30Hz...

Too bad that I missed that - although I'm not a "spectrum" guy, many of my colleagues have PhDs, and either design antennas and/or are radio propagation guys/gals. Many antennas designed here for space, for example. An oldie but goodie is the one that extends like a measuring tape - it was used on the Canadian Alouette satellite back in 1962 - not that any of these guys still are working obviously. Was able to view some of the first results of Radarsat 2, which was an education.

It is fascinating stuff, but not my field of expertise. (am coding Longley Rice propagation algorithm to run on GPUs, and did lots of verification of proposals for better Internet coverage in "underserved areas" across Canada but that is as close as I get). We do tend to take radio spectrum and antennas for granted, but as I am learning it is certainly not a mundane field.

Apologies for missing the opportunity to "one up" you!

Have a good new year, and looking forward to more of your words in 2016.


Jeff Dayman31/12/2015 19:40:34
2225 forum posts
47 photos

Andrew, you wrote:

"A practical issue with PEEK and Macor would be getting the thin wall needed at the exit of the divergent part of the cone where the steam jet mixes with the incoming water."

Purely as a technical discussion point, if you wanted to try PEEK for an injector I think you could easily injection mould PEEK to the sharp edged cone shapes you need, with very simple mould inserts. A side point to the discussion is that if the resulting injector functioned properly, making a bunch of parts for others or as replacements would be easy and relatively low cost once the mould inserts are made. Several hundred sets could be made in an hour after setting up and stabilizing the moulding press and process. PEEK is not easy to mould at home though, or cheap, compared to other thermoplastics. A proper injection moulding press with accurate, high heat, low shear nozzle, and precise injection pressure controls would be needed for consistent PEEK moulding and good quality sharp edged parts.

PEEK cones/internals for injectors would also never fur up with limescale either- virtually nothing adheres to it after moulding.

Just some food for thought, not suggesting anyone should do it, or throw out all traditional injectors....ahem

I have a lot of experience with injection moulded plastics in industry. Generally speaking I would never recommend plastics for steam service or for pressure vessels at all. However as internal parts in a metal bodied injector, PEEK may actually perform OK.

PEEK or any other thermoplastic should NOT be used as an injector body containing steam or water pressure or any other type of pressure vessel in my opinion.

Cheers and Happy New Year, JD

Andrew Johnston02/01/2016 20:51:31
6601 forum posts
701 photos

John: I'm not an expert on radio either, although it was radio that got me interested in electronics in the first place. I started buying "Everyday Electronics" when it was first published in the early 1970s. In one issue there was a design for a MW radio. It seemed magic to me that you could communicate over long distances using invisible waves. I never did get it working (for some reason known only to the designer it specified some really odd Ferranti semiconductors) but I then built a HF superhet, based around valves, which I did get working.

Up until the 1980s radio was quite a specialised area, mainly broadcast and military comms and radar. However, with the explosion of mobile 'phones and WiFi radio moved to centre stage. That gave a commensurate boost to salaries. And if you were into RF ICs then the sky was the limit! At the last consultancy I worked for the RF group got darn well paid, and were charged out at a much higher rate than everyone else. For some odd reason I acquired a reputation there as an RF troubleshooter. nerd


Harry Wilkes02/01/2016 21:31:30
1342 forum posts
65 photos

Interesting post but at the end of the day 'injectors' = pain in the butt wink


Andrew Johnston03/01/2016 10:14:45
6601 forum posts
701 photos
Posted by Harry Wilkes on 02/01/2016 21:31:30:

Interesting post but at the end of the day 'injectors' = pain in the butt wink

Which is precisely why I am trying to gain a better understanding of how they work and of some of the underlying theory. thumbs up


Andrew Johnston04/01/2016 12:11:23
6601 forum posts
701 photos

Jeff: It may be easy for you to injection mould PEEK, but I suspect rather more difficult for me! I've used quite a lot of PEEK in the past for custom coil formers and insulators in high temperature power inverters. It machines beautifully (like Delrin) but I've never tried moulding it. Some while ago I considering buying a small bench top injection moulding machine just to play around with, but I suspect they would be inadequate for PEEK?

If I get around to experimenting with injectors I had an idea to make the body out of a clear plastic, so it might be possible to see what was going on in the combining cone. Of course plastic plus high pressure steam is not a good mix. However, in an injector the only place where there is high pressure steam in the input to the steam cone. At the output the water pressure is also high, but the temperature isn't. Between the input and output the pressures are at, or below, atmospheric with moderate temperatures. So I would think that a plastic body should survive, at least for experimental purposes?


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