Porta's Derivation of Lempor Theory
February 9, 2019 at 4:27 pm #5093
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?
MartinFebruary 10, 2019 at 1:01 pm #5095
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
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.February 10, 2019 at 1:24 pm #5097
Porta wrote an introductory note which carries caveats:-
Introductory Note (added February 1999)
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.February 10, 2019 at 2:00 pm #5098
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?
ChrisFebruary 10, 2019 at 4:27 pm #5100
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!
MartinFebruary 11, 2019 at 8:37 am #5101
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!
ChrisFebruary 15, 2019 at 4:39 pm #5108
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.
MartinFebruary 16, 2019 at 9:15 am #5119
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!
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