**[Quoted from a letter sent by J.J.G. Koopmans to Dave Wardale dated 21 July 2005.]**

The following correspondence appears on this website at the specific request of Dave Wardale.

Whilst the extract quoted above is not a "question" (frequently asked or otherwise), the subject matter (and Wardale's response to it) are of such interest that they warrant inclusion in this FAQ section.

**Postscript:** Dave Wardale prepared a response to Jos Koopmans' thesis as published in his book "The Fire Burns Much Better ... ". This correspondence is available in PDF format through the following link.

J.J.G. Koopmans,

Venray, Netherlands

21 July 2005

Dear Mr. Wardale,

We have exchanged some correspondence in the past. As you may, or may not, remember, I have been busy writing a Ph.D. thesis at the University of Sheffield on the history of steam locomotive front-end development with an added goal to update theory.

As this is nearing its final date, I would like to give you an update on the results.

- Concerning the Lempor theory by the late Mr Porter (sic). This is rejected by the supervisors of the University. One of the reasons being that it is based on the historical concept of "Shock loss" which is not part of present day theory of fluid dynamics anymore.
- Concerning a replacement theory, a brief outline of a present day dimensionless approach to the chimney shapes concerned is attached. If there would be a course on this specific aspect of fluid dynamics, this is the way it would be taught to the University students.

Concerning the diffuser chimney part of the theory, there will he a problem. The Eu(ler) numbers calculated from the theory are the theoretical upper limits possible from a specific dimensioned layout. As far as I am aware, you have given some details of the 5AT front-end to Mr Peter Mintoft last year and he discussed this with me. From the requested vacuum of 5200 Pa and the steam flux of some 12800 kg/hr the Eu number requested can be calculated at 0.055. If the numbers are used in the Lempor equation to calculate dimensions, the orifice area of each Lempor would be 0.008 m, which you seem to confirm on the 5AT website. The Lempor mixing chamber diameter would be around 319 mm and the Lempor exit diameter some 573 mm. These numbers seem to be of the same order as those shown on the very small drawing of the website of Martyn Bane.

However, if these dimensions are used in the equation for a parallel chimney with a diffuser, as shown in Section 3 of the Appendix, the theoretical upper Eu limit can be calculated. This is only of the order of 0.045. This is less than you requested. A calculation for the SAR 26 type Lempor shows these numbers to be the other way round, requested 0.0475, theoretically possible 0.056, so it worked.

My firm conclusion is therefore that, based on the numbers supplied last year, which may have changed in the mean time, the steaming rate for the 5AT cannot be sustained by the Lempor system.

These conclusions are at present, only known by Mr Peter Mintoft, my supervisors at Sheffield and myself. From the 15th of September onwards, they will be known to the external examiners and, as I am preparing a trade edition of the thesis, to the peer reviewers.

Yours sincerely

J.J.G. Koopmans

**Dave Wardale responded as follows**:

26 July 2005

Dear Mr. Koopmans,

Thank you for your letter of 21st July, to which my comments are as follows:

- It is accepted that there is rarely a ‘last word’ to anything (the basic geometry of wheels seems to be an exception) and that it is therefore quite possible that current ‘state of the art’ ejector pump engineering knowledge may be an improvement over Porta’s own theories, such improvement being in the nature of a refinement. As a matter of interest, I myself queried the mathematics of the Lempor theory with Porta when I first became acquainted with it some 30 years ago, but did not receive a satisfactory explanation, and left it at that.
- Notwithstanding the above, or any ‘rejection’ of the Lempor theory by academics, it is an engineering fact that locomotive exhausts designed according to Porta’s work have proved more successful than any others. This practical experience is not to be dismissed.
- Practical experience has also shown that exhaust systems which have treated mixing ‘shock’ losses in the classical way have proved superior to those which have not done so. The former includes the Giesl ejector, the design of which is specifically aimed at minimising mixing losses. Whatever doubts one may have on the theory and assumptions on which the Giesl ejector is based, when correctly proportioned it has given good results at modest flow rates, its limitation at high flow rates being no doubt due to the high exit kinetic energy loss that is inseparable from a single chimney on a large locomotive (refer to page 473 of my book). This practical experience of the benefit of minimising mixing shock losses is also not to be dismissed.
- The currently preferred exhaust dimensions for the 5AT are in fact not to the Lempor theory but to the 1972 work of Kentfield and Barnes (The Prediction of the Optimum Performance of Ejectors. Proc. I. Mech. E., Vol. 186, London, 1972). This was one of a number of alternative works given to me by Porta, showing that he was open-minded to alternatives to his own theories. In fact it gives results which are remarkably similar to his own, which I think you would agree is quite significant and which implies that any rejection of the Lempor theory is also a rejection of this other more recent work, coming from a totally different branch of engineering. In the case of the 5AT an exhaust designed according to Kentfield and Barnes is marginally superior in terms of blast nozzle tip area to the true Lempor and has therefore been preferred, designated as a ‘modified Lempor’.
- I am confident that the 5AT exhaust will perform as predicted, because the established, service-proven theories say it will, and also because its dimensions are similar by both the two above-mentioned methods of calculation (i.e. they tend to confirm each other). Calculations of this nature, especially those for the input data, are not 100% accurate, and therefore do not preclude the possible need to optimise dimensions during tuning-up, as has always been common practice with locomotive exhausts (see (13) below).
- That parameters for the 5AT exhaust may differ from those of 3450’s does not surprise me, as by classical criteria the former is much closer to the ideal than the latter, which was subject to extreme height limitation for the mixture flow at maximum evaporation which in turn made it of necessity quite far from optimum proportions, and not to be taken as a ‘model’ design.
- The basic Euler No. is as you give it, but equating this to an expression containing terms from exhaust geometry is not necessarily rigorously accurate, as assumptions have to be made that are not necessarily true. I cannot confirm the correctness of your equations, the validity of which will need practical confirmation.
- Your analysis takes a value of blast nozzle tip area, An, without any consideration of how this area is constituted. You yourself have in the past put great emphasis on the value of multiple blast nozzles, yet this factor is completely absent in your Euler No. analysis. Although your letter states that ‘The Eu(ler) numbers calculated from the theory are the theoretical upper limits possible from a specific dimensioned layout’, the layout of the blast nozzles is in fact not specified. You may say this is not relevant for finding ‘the upper limit’, but consider that it is an established fact that, other things being equal in a properly proportioned exhaust, multiple nozzles do improve performance, i.e. give the same vacuum for a larger blast nozzle tip area, meaning with lower (time-average) exhaust steam velocity. This acts to increase the ‘requested’ Euler No. whilst at the same time it may, depending on the numerical values for the various interesting parameters, reduce the ‘theoretical upper Euler No. limit’ for the exhaust design, principally by virtue of an increase in Rn (it does actually do this for the 5AT Lempor). This somewhat curious phenomenon implies that according to this theory multiple nozzles would act to make an exhaust less suitable for its target, i.e. reduce exhaust system performance, which is the opposite of what actually occurs.
- The key to understanding this paradox appears to be the nature of the flow through a locomotive exhaust, which is not steady, as assumed in your work, but pulsating. Furthermore, most steam (and gas) flow is during release, at a (continuously varying) pressure which initially depends on the cylinder pressure at the time the valves open to exhaust. This being the case, all factors in your Euler No. equations, except those fixed by the exhaust dimensions, are liable to be different from the steady-flow values during release, which is when most of the gas pumping work takes place. Steady flow equations are therefore only an approximation for what actually occurs in a locomotive exhaust.
- A further factor that does not appear to be accounted for by your theory is the advantage taken of the pressure ratio across the blast nozzle being greater than critical during release, therefore giving supersonic exhaust steam velocity if the nozzles are designed to achieve this. Again, the effect of this will be to alter various parameters from their steady state values.
- The above points out basic limitations in the Euler analysis as you have presented it. It is true that other work, such as that of Porta, has been based on steady flow, but service experience under the actual flow conditions of a locomotive exhaust has proved satisfactory. Your ideas will have to be put to a similar practical test before they can be accepted. It can also be pointed out that those assessing your work must not only be knowledgeable in ejector pump design but also in the precise nature of the pulsating flow through a locomotive exhaust. It is quite possible that they are not – unless you are brave enough to tell them!
- As a matter of interest, Porta’s theories also make no allowance for multiple blast nozzles, but the work of Kentfield and Barnes does.
- The above has implications for any assessment of the present 5AT exhaust design on the basis of your Euler No. analysis. We can say that it is premature to jump to any conclusions about the performance of this exhaust on the basis of theory which, as I have explained above, must be regarded as only an approximation to what actually happens. For the record, quick calculations based on the actual 5AT true Lempor exhaust data (which is slightly different from what you assume) show a smaller difference between ‘requested Euler No.’ and ‘theoretical upper Euler No. limit’ than given in your letter, i.e. 0,052 versus 0,047, which, even if it were valid, would only translate into a small rise (approximately 10%) in back pressure being required to equalise the numbers, to be simply achieved by changing exhaust nozzle area during tuning up, whilst of course retaining the Lempor system as such (you have implied that the Lempor system per se would not be adequate). There would be a greater shortfall with the modified Lempor to Kentfield and Barnes, but all this is considered rather academic at this stage given the apparent limitations of the Euler No. analysis as an applicable criterion for the case in question, as pointed out above. If the theory can be made more rigorous, to account for the factors introduced by pulsating flow, and / or its validity demonstrated in actual practice, then it could be considered further at the detail design stage.
- The open question is always whether an alternative ejector can achieve the same gas pumping work with lower exhaust steam kinetic energy, i.e. with a larger blast nozzle tip area. You will recall that at the time of the 5AT exhaust design you were invited, through Mr. Mintoft, to design an alternative exhaust according to your ideas, for the same service parameters and dimensional limitations, for comparison purposes. This you were unable to do. No analysis, however erudite it may appear, is useful to a design engineer unless it can be used for design. Perhaps you may be able to put forward a detailed alternative once your thesis is complete, which would be welcomed, but until you can design such an alternative exhaust, showing a significantly larger blast nozzle tip area than that already designed, and back up your proposal with practical proof that it will work as predicted, the ‘modified Lempor’ will have to stand, and for the present time we had better leave it at that.

Yours sincerely,

D. Wardale