An essay on the front-end

All these three historical researches used steam with constant pressure in their models and regardless of differences in the model layout arrived at the same conclusion:

A half area orifice can create a vacuum of at least 70% of that of the original orifice.

This behaviour of the models needs an explanation. Because the orifice areas were halved models were used with a scale of about 70 % of the orifice. In these tests the pressure was kept constant however, and the steam should flow with the same velocity as in the case of the larger orifice. It passed a 70% model at 100% velocity, and as such it worked better than expected.

If we apply this situation to a locomotive front-end, suppose that we change our single orifice exhaust system into one that has two orifices but keeps the same total orifice area. All dimensions are therefore some 70% of the original. However because the piston does not feel any difference, the volume of the steam is the same, the total orifice area is kept the same, the velocity of the exhaust jet is the same in both cases. Because there is no such matter as model-steam or –smokegas all jets of any size are basically scale-models and have related proportions. In the vicinity of the two orifices the velocity of the jet is the same as in the single jet, the total perimeter however is 40% larger. If we look at the velocity at the tip of the core that still has the original velocity, in both cases at 4 times the orifice diameter from the orifice, the velocity distribution should be the same because of conformity. The cones surrounding the mixing jet between orifice and this position have in total the same area in both cases. However the same velocity took about 70% of the former time to travel through the smaller orifices to arrive at the same result. In the same amount of time the double chimney will therefore throw more smoke gases to the outside world.

This explanation is the proper one compared to the one stating that the circumference of the two smaller jets is larger. However the gain in circumference is offset by the loss in height! The superiority of a double exhaust in this case is therefore experimentally proven and theoretically explainable.

When an exhaust system is doubled a scale model appears. As explained in the example above the steam still flows at the original velocity as with the orifices scaled. However, if the velocity scale and diameter scale are made equal, a situation exists that is comparable to the original. The steam will take the same amount of time to pass through the model cone to the chimney throat as the original. Based on the volume passed we can calculate this scale:

scale * velocity * scale * diameter * scale * diameter * p /4 = ½* former velocity * former area. This gives: scale * scale * scale = ½, thus:

As a proof of this postulation the data of De Gruyter of the Staatsspoorwegen on Java can be used. He published his research of 1928 on front-end improvements of the 1200/50 Mallett compound locomotive class showing an improvement of 20% with a double chimney compared to the single chimney (Ingenieur van Nederlands-Indië, 1935 III, p.53). Also Ell showed in 1953 that a double chimney could have a larger orifice area, he gives the ratio of the double orifice diameters as 78.45% of the single one, experimentally deduced. Apparently these figures use about equal vacuum for both cases. The conclusion of this calculation is:

However this example does not stop with a double chimney. The same calculation applies to any number of orifices because the steam volume flows spread evenly through the orifices. The formula can therefore be rewritten as:

Number of orifices	formula	In %	Area increase	Virtual Diameter
1	1,000000	100%	100%	100%
2	0,793701	79%	126%	112%
3	0,693361	69%	144%	120%
4	0,629961	63%	159%	126%
5	0,584804	58%	171%	131%
6	0,550321	55%	182%	135%
7	0,522758	52%	191%	138%

As proof of validity the Lemaître exhausts of the 231.1251 series of the French Nord can be used. (Revue-Generale 1936) It had 5 orifices of 60 mm and a central one of 118 mm that could be closed. The calculated area of a single exhaust would be about 194 cm2. The Lemaître has about 250 cm2, an improvement of 30 %, which is rather low. The Bulleid Lemaître of the Southern only gives an increase of 14% in area. (Nock, The British steam railway locomotive of 1925-1965, p. 160)

Around 1980 the Garrat series of the 15^th and 20^th class of now Zimbabwe Railways received new six-fold orifices that had in total about equal area as the original single orifice but performed as well as the seven-orifice Giesl of the two test engines. (Durant, The Smoke That Thundered, p.129, 1997)

Giesl-Gieslingen tested his exhaust with 7 longitudinally placed orifices on the ÖBB 78.602 locomotive, the area could be increased from 123 to 232 cm2, some 80%. (Giesl-Gieslingen, Ära nach Gölsdorf, p.282). This is more in line with expectations, however Giesl data are to be used with caution.

The theoretical explanation of the functioning of the single chimney can be applied rather straightforward to a multiple chimney. If we consider a double chimney, both chimney walls will keep the jet from spreading. However if we could remove the wall between the jets, the velocity profile would not really change because the common boundary acts like a wall. The symmetry of the jets prevents further growth because there is an identical velocity equalisation from two directions. The profit is the removal of wall friction!

For practical reasons however a single orifice system with an existing chimney can only be replaced by one with up to seven orifices.

There is no special arrangement for more orifices to be made. In a round chimney the next possibility would be 12 additional orifices placed around the 7-fold, in total 19 orifices. This could only be applied in an oversized chimney like the Southern locomotives used.

Note 1. Care should be exercised when designing such a system. If a multiple unit is designed, each orifice should be carefully positioned in relation to the others. Every orifice should have about 8 times its area in a common chimney to properly shape its fluidics virtual chimney within the common steel boundary.

Note 2. In all these layouts the dimension of the bellmouth is to be regarded as related to the orifice diameter, its radius can be made smaller compared to the single orifice system.

Note 4. The orifices are calculated to be of the same diameter. If not fine-tuning must be used like the system of the Giesl exhaust, which needed it because the steam preferred the mid-orifices.

Note 5. The additional wall friction of a badly designed multi-orifice system will kill any improvement. The flow from the blastpipe into the orifice should be very free and carefully guided with internal streamlining; sudden jumps in total area should be avoided.

Note 6. It is easier to replace an existing orifice by a smaller one than to enlarge an existing layout. It has to be designed for the largest total orifice area (equal blastpipe?) and have the possibility to use smaller blast-caps.

Note 7. Giesl-Gieslingen has shown in his doctor’s thesis of 1929 that a chimney with its entrance very close to the orifices improves flow, the smokegas is forced to enter in the direction of the chimney. Co-flowing is better. All successful chimneys (Giesl, Chapelon, and Porta) use this principle.

In above description it has been assumed that a round orifice was used. However the research at the University of Illinois in 1933 seems to indicate that rectangular orifices give a slightly better performance. Rajaradnam also shows this. It is postulated here that this is so because of the tip vortices from the (sharp!) corners, these vortices would improve mixing.

It should be pointed out that under certain conditions it is possible to surpass the velocity of sound with the exhausted steam. This is when the blast pressure surpasses the critical limit, about 0,7 kg/cm². In that case a so-called de Laval nozzle, which narrows then widens, is of great value because it enables steam velocities above that of sound.

As can be realised from above description, chimneys that are designed this way differ from the Lemaître, Chapelon, Giesl and Porta types.

The Chapelon type, Kylchap, is a multi-stage exhaust system. A single orifice exhaust into a four-lobe Kylala spreader, the nozzles however are spaced too close together. It exhausts into a petticoat which finally exhausts into the chimney. Although it is a proven system, the mixing possibilities can be better. As discussed above a double chimney will always perform better, independent of its basic design. A double Kylchap, Kylpor or Lempor should therefore be compared on a single basis, corrected by 0.7937!

The Lemaître exhaust of the Nord 231.1251, as mentioned above, had a chimney throat of 544 mm, with an area of 2324 cm² and so 9,3 times the maximal area of the orifices. This is out of proportion regarding the steam to smokegas ratio defining this to about 8. Because the 5 circular arranged orifices are positioned at half the chimney diameter, they are also too far apart. Then also the orifices are 626 mm removed from the throat, just over half that distance would have been more appropriate. The low orifice area increase can be explained in this way. An extreme example is the Lemaître type exhaust, which was used by Bulleid for the Southern. It consisted of 5 orifices of 2+5/8 inch discharging in a chimney of 25-inch throat diameter. The original orifice was 5,5 inch, so the improvement was only 13%. The distance from orifice to throat was some 38,5 inch. The throat to orifice area is about 18 !! Also the throat to orifice distance should be less than half the present distance. The extremely large chimney counteracts a lot of possible improvements, so that the final result was not better than a double-chimney system.

The Giesl system is designed as a system of seven ejectors. As a consequence of the longitudinal layout the chimney has a lot of wall friction from the large sides although Giesl stated otherwise. A proper designed 7-orifice system in a round chimney would be better. Also his orifices are probably placed too close to each other and being longitudinally placed they do not work together beyond neighbouring pairs. Giesl used his own theory about shock-losses and used a very small throat to orifice area of about 4; this is contrary to the Zeuner theory. We have already noted that Giesl also stuck to an incorrect explanation of the Nozo-Geoffroy tests and these matters combined may explain why a Giesl exhaust could not be calculated for a larger locomotive like the SAR 25 series.

The Lempor system of Porta uses a number of above principles. His chimneys are calculated as large diffusors to give the best pressure recovery from vacuum to atmosphere. As such they lose velocity of the exhausted mixture, which the locomotive crew may not like as it hampers their vision. In a number of designs the jets are not parallel to the axis, but directed to the chimney wall. This gives a greater velocity in the perimeter, but a lower one in the middle; these effects probably cancel each other and mixing could be better. A double Lempor can be improved by using 7 orifices in each. Porta seems to take it for granted that beyond 4 orifices no improvement can be made. This and the position and inclination of the Lempor orifices needs additional explanation.