# Porta's Derivation of Lempor Theory

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• #5093
Martin Johnson
Participant

I have been studying in some detail the maths of exhaust systems. The usual derivations (E.g. ESDU 85032) invoke the following:
Conservation of Energy
Conservation of Momentum
Conservation of Mass

However, I cannot immediately see where Porta (his paper of 1974 available on Hugh Odom & Martyn Bane’s sites among others) has introduced conservation of momentum. Before I start a lot of equation juggling, has anybody worked where and how Porta accounts for conservation of momentum?

Martin

#5095
John Hind
Participant

Hi Martin – have you a copy of Jos Koopman’s book ‘The fire burns much better….’?

The book is useful in that lists and critiques the history of exhaust system development over the last 200 years. It also includes the various formula derived over the years for describing mathematically the workings of exhausts systems. It also includes the formulae derived by his PhD Supervisor – Dr Robin Saunders.

In the book he praises the Lempor Exhaust but like yourself is sceptical aboout the formula and points out a transcription error on the versions available on the web – if my memory is right a plus should be a minus or vice versa in one of the terms. He also reverse engineers the equation and concludes that it is the same as one developed by Zeuner in the 1850’s.

I used the equation, but put in realistic values for inlet loss and for diffuser performance taking into account diffuser geometry and correcting the transcription error. I developed a spreadsheet using the corrected equation and then developed graphs of draught for different steam rates. The graphs showed decreasing vaccuum for increasing steam and gas flow rates which is contrary to what is seen in real life. So I am sceptical of the equation and given time would like to use the same input data into other equations and see what the results are.

Others have used the equation and developed succesful exhausts, see this website

http://home.ca.inter.net/~mguy/A%20Lempor%20Exhaust.htm

There is a link in it to a Excel based calculator developed from the Porta Equation.

Despite our scepticism about the equation others have developed succesful Lempor exhausts. The Lempor we fitted to S160 has achieved its objectives of turning a poorly steaming engine in a better steaming one, which uses less coal than it did before. We had a one off chance to measure vacuum on it back in early 2017. We are in the course of doing similar measurements on a similar engine of the same class on another railway. To do these tests we are in the hands of the railway so progress is slow depending on locomotive availability and access to run trains.

The experience we have had with Lempor Exhausts is simlar to others who have fitted Lempor Exhausts, so despite the equation the Lempor Exhaust does work.

#5097
John Hind
Participant

Porta wrote an introductory note which carries caveats:-

This theory refers to the fundamentals defining the main dimensions of the ejector. It requires the calculation (or the obtention by experimental procedures) of the boiler characteristics, a serious matter in itself. It also presupposes that a large number of details coming from a long experience are to be respected. It does not include the swirl of both of the steam jet and the gas intake. Finally, a still pending serious problem is that it assumes that the flow is steady, non-pulsating, a field open to future investigation. It is not a “kitchen recipe” guaranteeing good results without a good tuning up with measurements. However, the reader may try, provided that if success crowns his trial and error, the merit is to be credited to the theory. If not, the Author expects that the failure is not to be credited to the theory, but to the user.

#5098
Chris Corney
Participant

Martin,

Looking at Equation A28.1 on page 446 of Jos Koopmans book “The Fire burns much better…”, Porta considers kinetic energy at each stage, however he also includes terms 2 and 3 which cover the shock losses included in the mixing chamber. Am I correct in thinking that these terms would allow for the difference between the results obtained by conservation of momentum and conservation of energy?

Chris

#5100
Martin Johnson
Participant

Thank you both.
John, I am aware of the caveats around the method. Also despite my scepticism, there is no doubt that the multi nozzle, long diffuser arrangement is going to give a good account of itself (E.G. Young proved that in 1930). I have rather more scepticism about trans-sonic nozzles, kordinas and converging mixing chambers.

Chris, Many thanks for the links, I shall investigate further. I don’t have JK’s book. I read his Appendix on model locomotives in a borrowed version, which was enough to convince that the money would stay in my pocket.

Don’t I sound like a crusty old fart these days!

Martin

#5101
Chris Corney
Participant

Hi Martin,
I thought that JK’s book was very good as a historic record, and useful as piece of reference material, but if you are looking for a textbook on fluid mechanics, there are better options available.

Regarding nozzles etc., in my mind the jury is still out until we can get some decent test results from a main line sized locomotive such as an S160. There are some people putting these sort of devices on locomotives with slide valves and saturated boilers, which is probably a waste of effort.
On the other hand, some people would say that messing about with steam engines is a waste of effort!

Regards
Chris

#5108
Martin Johnson
Participant

Hi,
First, an apology to John (not Chris) who provided the links to other work on Porta arrangements. I have had a quick skate through spreadsheet link that John gave. It looks to be a fairly “verbatim” implementation of Porta’s paper, although the method of looking for a minima in the nozzle area is interesting. The section devoted to calculating steam flow is rather less good, relying on calculating cylinder swept volume, cutoff etc. but taking no account of superheat and hence condensation losses (missing quantity). Hence comparing “Romulus” (a wet design, if I remember correctly) with other superheated, full size engines is going to be rather suspect. There is also a fixed view (although the value is user settable) of gas to steam ratio. That ratio does vary, increasing as greater superheat is introduced – simply because more of the flue gas is being used toward superheat and less at evaporating water. It also varies with locomotive size – my own analyses shows that the air to coal ratio in models is significantly greater than that in full size.
All grist to the mill, though.

Martin

#5119
Chris Corney
Participant

Hi Martin,

Good points,we should also consider how much steam is used by auxiliaries (injectors etc.) and doesn’t pass through the blastpipe, and then there is leakage!

#5121
Martin Johnson
Participant

Yes Chris, all those “losses” need to be subracted off the exhaust steam mass flow.

And then there is the combustion gas flow, for which Porta does give some suggested “Design Allowances”. There is also the following to consider:
1) The air to coal ratio increases significantly at lower grate loadings, thus increasing the combustion gas to steam ratio. Question – does the flat out condition actually represent the worst design point?
2) Similarly, the resistance through ashpan, grate, firebed, tubes, cinder catchers (if fitted) etc. varies broadly as the square of the gas flow. However, the firebed thickness also tends to vary with grate loading so that changes more as a linear relation(???).
3) A significant proportion of the coal goes up the chimney unburnt – especially at high grate loadings. Moving that mass of unburnt coal eats up momentum from the steam blast. We are effectively pumping a two phase fluid / solid mix with a density over that of combustion gas. Should that represent the design point?
4) Then the system needs to be controllable – so there must be allowance for a pressure drop across ashpan dampers – even at flat out condition.

As to the real importance of those factors (and others, no doubt), I don’t know until I start doing some sums.

Martin

#5122
Chris Corney
Participant

Hi Martin,
Yes, it’s all very complex. I think it would be an acheivement if calculated values could approach those achieved on the road.
I forgot to mention the Gas Producer Combustion System (GPCS), if used.
A proportion of the exhaust steam is added to the combustion air. This reacts with hot coal to produce Hydrogen and Carbon Monoxide, which then burn back to carbon dioxode and steam in the combustion chamber.
This obviously reduces the blastpipe steam, but adds to the mass of the combustion gas flow.
Regards
Chris

#5132
Martin Johnson
Participant

I have been doing some data mining on E.G. Young’s paper of 1930. First step – what is a realistic Cd for a steam nozzle? I have accounted for velocity pressure in the pipe where (I have inferred) Young took the pressures and come up with a scatter around 0.85 for all the nozzles which underwent extensive testing. The “Pepperbox” averages 0.78.

Now the proportion of energy used is Cd ^2, so about 70 to 65% of the incoming energy is being usefully turned into velocity energy. That still leaves at least 30 % which goes to increase the temperature, and hence the specific volume, and hence the velocity of the remaining gases, leading to even more energy going up the chimney to waste. So a properly designed blast nozzle is essential. It is quite possible to design nozzles with Cd values up around 0.95 but they tend to need axial length – which is what a steam loco seldom has available.

That leads on to another observation – neither Porta or ESDU 85032 calculations account for density and temperature changes due to increasing entropy of steam and gas. I believe the latter to be insignificant, but the former would give around 8 degrees increase in steam temperature. Not large, but it can be accounted for.

I have also continued attempting to resolve Porta and ESDU 82032 – without success. I cannot see where Porta accounts for momentum.

Martin

#5133
Chris Corney
Participant

There is plenty of evidence of spark-throwing by locomotives, in other words particles of burning coal going up the chimney. I don’t know what the effect the heat produced by this combustion would have on draughting.

#5171
Martin Johnson
Participant

I have been looking at work by Nigel Day on the Porta type of design. He strongly advocates divergent nozzles at a 7.25 degree outward splay. Which seems to be what was done on the ASTT S160 design.

Simple question – Why?

Martin

#5173
Chris Corney
Participant

Hi Martin,

Sorry for the delay in replying.
I think some people hold the view that the jet should “bounce” off the sides of the mixing chamber.
My thoughts on the operation of the ejector are based on Bernoulli’s theorem and the conservation of momentum. Others seem to support the “turbulent entrainment” theory. I suppose that there needs to be sufficient mixing to obtain a reasonable velocity profile in the diffuser to prevent recirculation, and this will inevitably produce some turbulence, but otherwise my view is that turbulence should be kept to a minimum.
Best Regards
Chris

#5174
Martin Johnson
Participant

Hi Chris,
I had read this “bounce” stuff in Nigel Day’s writings, which claims that only those with understanding of boundary layers would understand it. But that is as scientifically rigorous as Abracadabra or perpetual motion. There do not seem to be any comparitive tests (physical or CFD) of axial or splayed nozzles. If anybody does know of such tests – please declare it!

I also have problems with supporters of the “Conservation of Momentum” supporters taking on the “Bernoulli” supporters in some kind of pitched battle. In my universe, universal laws are universal and do not give way to other laws on a whim or fancy – In short both C of M and Bernoulli must BOTH apply at all times in all situations.

So, you asked for my views. I think the splaying of the nozzles might be a method of injecting higher energy fluid toward the walls of the mixing chamber and diffuser. Higher energy fluid at the wall would help to suppress flow separation at the transition from the mixing chamber into the diffuser. If you look here http://www.thefireburnsmuchbetter.nl/ at the bottom left sidebar “Lempor CFD?” then go to the first CFD velocity plot, there is dark blue at the walls as the mixing chamber transitions to the diffuser – as you would expect. That indicates incipient flow separation in the area, which means the diffuser is not working as well as it could. (Actually when I stopped working, CFD had not reached a stage where it could RELIABLY predict such separations, because you need a very fine grid in the area of separation to accurately predict the separation; a point that I suspect is still conveniently forgotten).

However, in the extreme case of an annular jet pump (driving fluid injected in an annular ring around outside of pumped fluid) the peak efficiency drops a little – source ESDU report 85032. On the subject of conventional multi nozzle designs, ESDU 85032 says “the nozzles should be spaced equally across the mixing chamber entrance and should not be placed so as to form a ring close to the wall as this arrangement reduces efficiency”

I have found in the layout of nozzle for my own steam lorry design that splaying the nozzles and just drawing out 1 in 3 steam cones, suggests a “hole” in the steam between the four jets, which would persist well into the mixing stage.

Hence my simple question – does anybody know why we are doing it? The ASTT obviously believe in the theory as it is incorporated in the S160 lemporta design.

Martin

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