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I’m wondering if it would be worth writing up your findings for future reference by other members of the group.
I’m working on it Chris, but these things grind awful slow when you have a steam engine to build.
I have just found a mathematical error in my comparison of momentum and energy approaches. (Missed a divisor of 2 in one of the energy terms!).
What I now have is exact correlation between the momentum approach and the energy approach as set out by Porta. (Which he does hint at in his 1974 paper, but gives no proof.) At present this is limited to an analysis of a parallel chimney, since my aim was to investigate differences in approach, and tapered chimneys complicate matters dramatically.
So, it doesn’t matter which way you go, it comes to the same answer.
(One happy bunny)
Broadly speaking, you have it about right, Chris.
In the case of a loco front end, the efficiency is actually miniscule when viewed as a pump. So any attempt at using energy as the main consideration means energy in is a large number – probably known. Losses are a large number but can be estimated (more or less!). The output is a small number, being the energy in minus the losses. However, any error in the other two terms will cause huge errors in the output.
Typical numbers for a Black 5, expressed in megapascals – 340 energy in. 30 out, hence losses in the order of 310.
One has a similar problem with the momentum approach, but are not faced with trying to estimate loss terms for sharp changes in velocity (Particularly Terms 2 & 3 of equation 1 in Porta’s 1974 paper). Here, momentum expressed in megapascals – 210 momentum in, about 30 out.
As far as I can see, the energy approach will give a smaller blast pipe orifice just running some typical numbers, but if you work it all back the difference between approaches is quite small (about 5% on diameter for the Black 5 example). Hence the reason why the Strahl / Porta approach “works”.
I have found the answer to my original question and it is this:
Porta’s formula is derived from Strahl’s which is derived from conservation of energy.
The more usual formulation (such as ESDU) is derived from a consideration of momentum conservation.
Prof. Bill Hall points out that in a system such as a loco front end, the losses are so great that working from energy conservation means any minor errors in determining the energy input less the energy lost in “shock losses” means major errors in the remainder (which is what we are interested in). That is why Hall (and others) favour the momentum approach.
It does beg the questions – what is the mathematical difference between the two approaches? Which gives the “safer” design? And is the difference significant for the typical quantities experienced in a loco front end?
I am not aware that anybody has worked through those questions.
Have been out of circulation for a while, and then locked myself out of my account one here!
Anyway, to pick up on your recent posts:
Koopmans says “It is conceivable that a properly designed petticoat could act as a sequential ejector.” – Is that not a Kylchap, which we were discussing right at the top of this thread?
I’m thinking that the design of the Kylchap, with the various cowls and mixing areas would have maximised the effective surface area of the steam jet, and therefore minimised the “lost” KE of the perpendicular moment of flow. – Maybe. I come at it from the ESDU graph, which shows that as the steam / gas mass ratio moves lower, the area ratio increases and the peak efficiency will increase – which seems to be the question you are posing. Whether or not the efficiency increase is due to the mechanism you postulate I can’t say for sure, but it looks reasonable.
Further to the above post, I came across some data for a Class 6 locomotive, and at the maximum boiler output this quantity would be of the order of 50kW. – Yes, quite a lot of power and when you factor in the jet pump efficiency, thats at least 150 kw off the DBHP!
If you take the pulsing effects into account it could easily be double this value. I think that is a very valid point. The “oft quoted received knowledge” is that the pulsation does not have a measurable effect. However, I think that is mis-leading. The pulsations affect the nozzle peak Mach number, the kinetic energy loss, the porosity of the firebed, and IMHO the tendency of the fire to lift, the loss of unburnt fuel.
Shape of Mixing Chamber – I am currently reading a paper on air ejectors by LJ Kastner & JR Spooner on air ejector design. They make the point that you can design (and calculate) on the assumption of constant pressure mixing (which gives a reducing / expanding chamber) or constant area (parallel chamber) or indeed any combination of the two. They make no conclusions about which might give better efficiency. The paper can be found here:
It is interesting in other respects:
Convergent – divergent driving nozzles were not found to be best for transonic flow in the driving nozzle.
The theory advanced takes account of increasing entropy in the driving and mixing sections (which Koopman & Porta do not)
It confirms that a diffuser taper of 5 to 10 degrees included is the right range – even with the highly disturbed entry flows.
Chimney Machining – What size chimney are we talking about? If full size, I would suggest casting would be the way to go for complex shapes. That being the case, the problem resolves into making the corresponding male shape which is easy. For model work, boring bars are best if kept to a length / diameter ratio of 5 to 6 max. Even in my wee shop, my biggest boring bar is 25 diameter, giving about 6″ of reach, but remember that reach goes up with the size of hole being tackled.
Hyperboloids – an interesting concept. As to manufacture- for chimney or nozzles the internal form woud these days be cut on a CNC lathe, feed in the co-ordinates and there you are. For those of us working without CNC you carefully mark out or otherwise cut a form tool of the correct form and use that in a lathe.
I take it you also mean the nozzles would be arranged pointing in a “helix”. Producing a nozzle block with seatings for such nozzles is also reasonably easy to manufacture – really no more difficult than the splaying out nozzles of the S160 exhaust shown on this site.
Benefits – they would be quite subtle I think, but you do get more path length of the steam jet for a given height before entering the mixing chamber; so it helps to solve that eternal fight against vertical height to keep within loading gauge.
Thanks for the reply.
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.
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?
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.
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.
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.
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!
That starts to make a bit of sense – provided there is a sharp enough exhaust to get sonic velocity at some stage. Those S160 results are going to be very interesting in that respect.
Well yes, that might be so. But an offbeat engine means the valve events are not as they should be, so more energy is going up the stack and less into turning the wheels. Therefore, more energy is being expended in the blast pipe, meaning more energy to draw the fire, to make more steam to feed that hungry off-beat engine.
As to the relative merits of a Jube Vs. a Black 5, I do not really know enough detail of the two designs to comment.
I remain un-convinced that peak flow through the blast is a good thing. The more “peaky” the flow, the more likely you are to be running part of the cycle in the sonic regime. However, if you can smooth things out, you should be able to run the whole cycle sub-sonic. The attraction of sub-sonic is that a basic contracting nozzle will work well across the whole flow range. Once you start putting DeLaval nozzles on, it will be great if you get sonic velocity at the throat, the expanding section will INCREASE exit velocity. However, if you do not get sonic velocity, the expanding section simply re-expands the steam and you DECREASE exit velocity. So at anything below design point, you are making things worse, not better – unless somebody can explain how they have matched a DeLaval nozzle to the draught requirement ACROSS THE WHOLE OPERATING ENVELOPE then I maintain it is not the way to go. Porta certainly does not touch on this subject, nor E.G. Young. Any suggested reading for me?