An essay on the front-end

Jet theory has been treated in books by Pai (1954), Abramovich (1963) and Rajaratnam (Turbulent jets, 1976). Rajaratnam is also co-author of the Handbook of Fluid Dynamics (1998), his theory is up to date. Details of the functioning of a jet can be observed from the flames of a burning kitchen stove. From the outside the turbulence of the combustion products is seen. Further inwards a bright blue inverted V shaped part of the jet exists in which the gas is sufficiently mixed with the outside air to burn. On the inside a colourless cone is to be seen, about 4 times the width of the orifice long, with straight sides and pointed top containing the unmixed gas at the original velocity. This picture is typical for any jet. When it flows from its orifice it start to mix with the surrounding gases thereby widening while at the inside, to about 4 time the orifice diameter, the original velocity in maintained. The mixing process is very turbulent because when the jet comes out of the orifice a large "shearing stress" exists between the large velocity jet and the surrounding stagnant gas mass. What happens then can at best be illustrated with 3 layers of foam-rubber/plastic on top of each other. When the lower and the upper layer are pulled in opposite directions the middle layer starts to curl at both ends. This is about the process that takes place, however along the sides of the curls at once the process is repeated resulting in the large cauliflower type of exhaust steam shapes that most people identify with steam locomotives. The curling/rotating part of the process is very essential, without it is impossible to get the mixing process that is needed to rotate the smoke gases into the jet and out of the smoke box. As has been stated before the velocity profiles in the jet are Gauss shaped curves, measurements and calculations have proved this. The pressure distribution around the jet shows that accelerations take place in the surrounding gases because locally an under-pressure is measured around the jet and certainly close to the orifice. In the direction of the jet the velocity along the axis is at first constant to about 4 orifice diameters after which it starts to degrade by imparting momentum to the surrounding gases. After about 6 diameters it can be shown that the axial velocity profile is related to the distance to the orifice, the axial velocity distribution is shaping into a hyperbolic relationship. The proof can be found in the books of Abramovich or Rajaratnam about jets.

In a front-end the exhaust jet is directed into a chimney. The chimney entrance should have a very smooth entrance; any data book on engineering shows entrance coefficients. A large bellmouth type performs best. Within the limitations of the chimney walls the jet cannot spread any more but the turbulent mixing will continue as long as velocity differences exist. Near the throat of the chimney large accelerations are therefore possible for the gases in the perimeter. Here again a large local vacuum can be measured. In the books this case is not fully covered, Rajaratnam shows however that an erroneous co-flowing design can create a large entrance vortex, seriously hampering the flow. However this case is prevented when proper chimney dimensions are used.

In general, numerical calculations in fluid dynamics are governed by the very complicated equations of Navier-Stokes. However in the case of the jet only motions in one direction are considered so that this case simplifies to a description of the momentum imparting mechanism. If we think of the jet as being divided into a number of concentric tubes we can calculate the amount of momentum that is carried through the "wall" of each tube. In line with the turbulent mixing phenomena mentioned earlier it is assumed that under the condition of about equal specific weight, including temperature effects, the momentum can be divided between the tube (element) under consideration and the next one. The process is calculated sequentially from inside to outside and so the momentum is carried outwards until the velocity calculated equals f.i. 0.001 of the starting velocity of the calculation. This process is repeated a few thousand times after which a large number of calculated velocities is available. However the real position of any calculated velocity is not yet known. The process calculates sequentially, while in reality a complete velocity distribution is developed in parallel, at the same time. However it is assumed that all calculations describe a process that takes equal time for all evaluations. A velocity distribution can therefore be considered to consist of elements that have been calculated in an earlier or later iteration. If n is the iteration number between 1 and say 6000, and j the present step outwards, the neighbouring elements of element V(n,j) of velocity distribution n would consist of V(n+1,j-1) and V(n-1,j+1). The velocity distribution elements so constructed are compared with those from the Trüpel test and can be matched, the assumption is a valid one.

As in all other comparisons between theory and practice the calculated velocities in axial direction have to be compared with test data, here again Trüpel is used. With the data available a best fit can be calculated between the calculated and the measured axial profile. After this the calculations show a very good match witch the measured data.

Because of the nature of this elementary calculation process it is possible to calculate the effects of artificial boundaries like chimneys on the behaviour of the flow. The flow cannot pass a boundary so that the velocity profile tends to develop into uniform velocity as also is shown in practice. Because the method looks like methodical bookkeeping for the velocity distribution a number of other processes can use the same method, the amount of entrained smoke gas can be permanently evaluated and also the temperature of the mixture can be calculated. The local pressure however still gives problems.

We should realise ourselves by now that the behaviour of the jet is totally dictated by nature. It cannot be changed. One of the few possibilities left is dividing the jet and change the shapes of the metal surrounding the jet(s) and their relative position and it took engineering artists like Chapelon, Lemaître, Giesl and Porta to sculpture their designs.

Chapelons front-end exhausts from a single orifice, the jet that already accelerates some gases is then directed into the fourfold Kylala orifices that act as a spreader. The four jets, already containing smoke gases, are blown into a petticoat, the upper part of which acts again as an orifice that finally exhausts into the chimney. Basically the Kylchap is a multiple exhaust arrangement in which the jets do have different velocities. The Lemaître has five orifices plus a central adjustable one with a wide chimney.

The Giesl exhaust has seven orifices that are placed longitudinally and relatively close together. The typical Giesl chimney is designed to act as a sevenfold ejector and has its narrow throat close to the orifices. Thus the local vacuum around an orifice and that of the chimney throat are combined with the aim of making it so large as to effect the flow of smokegases to the chimney. A typical Porta chimney has multiple exhausts into a round chimney that has its throat placed close to the orifices. The four jets that exhaust into a round chimney will help each other to change into uniform velocity more quickly.

In the past most locomotive manufacturers and design offices of railways must have had some idea about the correct dimensions of the blast-orifices of their steam locomotives. Although some suggestions can be found in the railway magazines, real data is hard to get .

However Nordmann of the Deutsche Reichsbahn published a formula in 1930 ( Organ fur die Fortschritte des Eisenbahnwesens, 1930,p.1505) from a plot of data from a number of locomotives. He said that the area of the orifice, in cm², could be 40 + 0,62 * evaporating area in m². Henschel used the formula until the last Taschenbuch of 1960. S.O. Ell in England (Journal of the Inst. Of Locomotive Engineers, 1953, p. 561) published also a formula, which in metricized form could be: 60 + 0,4 x evap. area in m². Ell probably used only data from the larger superheated BR locomotives; the smaller and older types were probably not included. In the Netherlands a list of all orifice dimensions was published in 1935 (Handboek der Spoorwegen deel III, p. 136). Using the data in a spreadsheet including figures about superheating and grate size with a linear estimation function gives something like 36 + 0,605 * evap. heating area. By using the Excel possibilities of multiple regression it can be proven that grate size and superheat do not account for large differences. The evaporating heating surface defines solely the orifice area from a regression point of view. However these results should be used with caution. The front-end of a number of locomotives had serious deficiencies, leading to a too small orifice area. In general these formulae should be used to calculate the area as a first approximation from which an optimisation could start.

Over the years a number of improvements was gradually made in the orifice/chimney layout. As mentioned earlier a description of the optimal dimensions was given in the 1917 "Railway Engineer". In slightly changed form S.O. Ell repeated it in his 1953 paper. The throat of a chimney was to be about 2,85 the orifice diameter, the distance from the orifice about 2,1 throat diameter. The chimney had to have a large bellmouth entrance and should have 1:14 taper along a length of minimal 26-inch. These dimensions are explainable. The steam to smoke gas ratio is of the order of 1:1,5 to 1:2. A good figure is 1.85, some 20% air excess on the theoretical real need. Because their respective specific weights do not differ much in an momentum exchanging device, as the front-end is, the resultant mass of about 2,85 times that of the steam is moving with a velocity of about 1 /2.85 of that of the steam. In a closed system the area through which the mixture had to pass would indeed have an about 8-fold area, 2.85 times the mass at the inverse as the velocity. Also the bellmouth entrance is a must, any engineering manual list entrance coefficients, this type works best. The taper was found from practical experience, however research in the 20-th century has shown that along the walls of a flow a gradually increasing stagnant sublayer is formed. The taper of the chimney counteracts this effect. Because a well designed chimney shows a throat vacuum of twice that of the smokebox, it cannot be stressed enough that a proper shape is extremely important for the complete system. These figures can be regarded as the present-day representation of Zeuners theoretical formula.

The value of throat to orifice area of about 8 is used by Ell and can be found in Porta’s publications. Also Wardale prefers this figure. Giesl however uses this as upper limit in his designs, when the orifices are opened up, throat remains constant. He tried to push his mixture through a too small throat, creating a traffic jam as it were.

Almost all engineers who have applied multiple exhausts have been rather silent about the underlying principles and theory, whether they are Chapelon, Lemaître, Giesl or Porta. The available historical articles deserve some closer inspection.

As noted earlier already in 1852 Longridge stated in a lecture before the Inst. Of Mining Engineers that a double chimney would work better, he had found this by improving his ejectors for mining ventilation. In 1863 Prof. Zeuner proved this in his book "Das Lokomotiven-Blasrohr".

He showed in table III on page 37 that an orifice of half the area fed with steam at the same pressure of the full orifice area always resulted in more than 50% of the smokebox vacuum, even up to 80%. This result seemed to have escaped notice; the tests of Zeuner have always been listed as insignificant because he used very small sized orifices, 10 and 14,14 mm, unrealistic backpressures and very wide chimneys.

0,574	0,800	0,486
Average	Maximum	Minimum
0,552	0,596	0,686	0,771	0,800
0,486	0,506	0,550	0,577	0,580
0,491	0,500	0,530	0,542	0,564
0,490	0,496	0,509	0,510	0,529
0,572	0,567	0,578	0,577	0,594

0,569	0,629	0,719	0,753	0,793
0,535	0,559	0,584	0,618	0,624
0,507	0,515	0,541	0,563	0,588
0,509	0,510	0,538	0,562	0,572
0,560	0,575	0,575	0,572	0,574

0,573	0,623	0,721	0,754	0,762
0,528	0,537	0,578	0,585	0,589
0,526	0,528	0,555	0,577	0,603
0,520	0,521	0,536	0,543	0,572
0,543	0,547	0,563	0,575	0,577

0,577	0,615	0,698	0,733	0,746
0,516	0,521	0,547	0,558	0,567
0,513	0,518	0,536	0,557	0,569
0,522	0,519	0,526	0,548	0,562
0,518	0,524	0,531	0,535	0,537

Comparable results were also found by Nozo & Geoffroy in 1864 (Mémoires et comptes rendu des travaux de la Societé des Ingenieurs Civils, 2 ser.16. ann, 4 cah, p.271).

Copy of the original table D of the measured data of Nozo & Geoffroy.
(click on image for full-sized version)

The caption on the left it says "Pierced plate of 10,20,30,40,holes of 0.009m". The captions above the columns are: area of the holes, the diameter of the orifice, area, pressure in mm mercury, weight of steam, chimney area giving best results, vacuum in mm H₂O, weight of air drawn, ratio’s of chimney to passage, of orifice to chimney, of passage to orifice, air to steam.

Nozo and Geoffroy used 10, 14, 20 and 28-mm orifices in a model of a front-end. However they also tried to define the optimum area of their chimneys in relation to the orifice area. Also these tests were labelled as insignificant due to the small orifices used. They tested multiple orifices but before they had researched their optimal combinations of orifice and throat, as could be expected their results were not spectacular. Nozo and Geoffroy were the first engineers to try a four-fold chimney on a Crampton locomotive of the Nord in France

However in 1895 Troske (Glaser’s Annalen 1895, p.24) used a 1 to 1 scale model with real-size orifices of 100 and 140 mm, he got the comparable results, see the table on (his) p. 102.

The caption is: Tapered chimneys of 1/12 inclination. The chimney diameters are 300 to 400 mm, the measuring spots are start, throat and end of the chimney. The vacuum is given in mm watercolumn for orifice diameters of 100 to 140 mm.

The table shows a ratio of 0.816 on average, a maximum of 0.913 and a minimum of 0,694. Please note that the Zeuner relation between both masses and the areas means that the smaller, better performing, orifice needs a larger chimney area, not a modelled one.

	avg		max		min
	0,614		0,861		0,438
82		65		27
60	0,732	42	0,646	18	0,667
32	0,533	26	0,619	12	0,667
23	0,719	17	0,654	7	0,583


337		202		84
253	0,751	174	0,861	60	0,714
135	0,534	100	0,575	32	0,533
80	0,593	48	0,480	14	0,438

786		682		255
650	0,827	435	0,638	153	0,600
384	0,591	256	0,589	79	0,516
206	0,536	135	0,527	37	0,468

114	141	0,809	0,816	avg.
124	144	0,861	0,913	max
100	112	0,893	0,694	min
103,5	133	0,778
117,5	138	0,851
105	115	0,913
93	124	0,750
111	134	0,828
104	119,5	0,870
82,5	114	0,724
105	130	0,808
101	120,25	0,840
71,5	103	0,694
96	120	0,800
96	118	0,814