On the Expansive Working of Steam in Locomotives. By Daniel Kinnear
CLARK, C. E.-(With a Plate.)*

[Abstract of a Paper read at the Institution of Mechanical Engineers.]
Continued from page 11.

It is now proposed to consider the conditions on which the expansive working of steam in locomotives may be most beneficially carried out. The condensation of steam in the cylinder by exposure, which takes place in certain arrangements of locomotives, is susceptible of proof in various ways: by the internal evidence of the indicator diagram, in respect of its general form, the form and course of the expansion line, and the back pressure; also by a comparison of the volume of sensible steam which is found to pass through the cylinder, with the volume of water found by measurement to be consumed from the tender and the boiler. The evidence of the expansion line of the indicator diagram will be first considered, both for well protected and partially protected cylinders.

Evidence of the Expansion line of the Indicator Diagram.-As the total heat of saturated steam is nearly constant for all pressures, being slightly greater the higher the pressure, there can be no condensation of steam during expansion, in a perfectly non-conducting vessel, but rather a slight surcharge. The surcharge is so slight, however, as not to require further

• From the London Civil Engineer and Architect's Journal, September, 1852. VOL. XXV.-THIRD SERIES.-No. 2.-FEBRUARY, 1853.

7

notice in the present inquiry; we are only concerned in showing that perfectly protected steam under expansion, without any deduction from, or accession to its heat, continues substantially in a state of saturation, and unaltered in quantity or mass; and that if the indicator diagram show that at the end of expansion the final quantity of sensible steam is either greater or less than the initial quantity at the beginning, and surcharge by condensation or otherwise must have taken place in the condition of the expanding steam. The initial and final quantities, or their equivalents in water, are readily found by dividing the capacity of the cylinder and the clearance occupied by the steam, by the relative volumes due to the initial and final pressures. By the same law we may find the expansion curves, which would be described with a constant quantity of saturated steam under expansion; this has been done for the slow diagrams from No. 13, C. B., (Plate I. fig. 1,) and the curves of simple saturation thus found are shown in dotting. The deviations of these from the actual curves are all referable to one cause-the condensation of the steam.

In No. 1, the cylinder must have been at a lower temperature than the steam during the admission, and some condensation must have taken place, for no sooner is the steam cut off, than condensation is made visible by the sinking of the expansion curve below the standard throughout the whole of its length. In No. 2, also, this takes place to a small extent for the first half of the curve, when the temperatures of the steam and the material of the cylinder become equal; after this, as the pressure continues to fall, and the temperature of the steam with it, the curve rises and meets the standard curve at the end, in virtue of a partial re-evaporation of the steam previously precipitated, caused by the cylinder itself, which, colder than the steam, and heated by it in the first stage of the expansion, is now relatively hotter, and partially restores the heat of which it had previously robbed the steam.

In Nos. 3 and 4, the process of successive condensation and re-evaporation is still more distinctly brought out. In these cases, the greater portion of the heat engaged in the restoration of the steam during expansion must have been absorbed by the cylinder, by condensation of the steam during admission. Under the 3d and 4th notches, the observed final equivalents are shown to exceed the initial by 19 and 45 per cent. of the latter respectively; which proves that, in the two cases, at least 19 and 45 per cent. of the steam admitted must have been condensed during admission, as the additional steam can have been obtained from no other source. Although the actual expansion curves, Nos. 3 and 4, indicate much higher mean pressures during expansion, than the standard curves, and may so far be viewed as superior results, the favorable difference is only a partial amends for the much greater loss by initial condensation; and an expansion curve may be constructed backwards, in terms of the indicated mass of steam at the end of the expansion, to show from what initial pressure this mass of steam could have expanded, had there been no condensation. Take No. 4, for example. The final pressure at G is 13 lb., for which the relative volume is 939, and the ratio of the initial and final total volumes, or the degree of expansion, is 1 to 2:66; then 939 2·66353, which is the relative volume for 66 lb. steam at the point of suppression. Tracing the expansion curve G H for this pressure, as in the drawing,

for which any number of intermediate points may be found in the same way, and drawing a horizontal admission line H I to the beginning of the stroke, the extra shaded area so inclosed is a representation of the real loss incurred by initial condensation of the steam; and, without going into figures, it appears nearly as much again as the area or power actually obtained.

The diagrams just discussed are, of course, extreme cases, which might occur in any cylinder, outside or inside; and they have been selected simply for purposes of illustration. They have served to show in what way the expansion curves of indicator diagrams may be turned to account in developing the condition of the steam. Our business is now to find to what extent, in the ordinary working of locomotives, the condition of the steam is affected by the circumstances of the cylinder.

The first point is to show, by the expansion line, that in well protected cylinders the steam is not subject to condensation. Referring to the 26 diagrams obtained from the Great Britain, of which the cylinders are suspended in and freely surrounded by the hot gases in the smoke-box, it appears that for each notch the influence of speed on the relation of the initial and final water equivalents of the steam expanded is nearly inappreciable. Dealing therefore with the means, the mean differences by which the final are less than the initial equivalents are

For the 1st notch 3 per cent. of the initial equivalent.

These per centages are practically nothing, and the virtual constancy of the mass of expanding steam during expansion, thereby proved, shows that for the greatest observed degrees of expansion in the cylinder of the Great Britain, no change in the condition of the steam is observable, and that there is, consequently, no condensation at all.

Experiments made by the writer on some of the engines of the Edinburgh and Glasgow Railway, with inside cylinders, lead to the same conclusion.

Numerous diagrams were obtained by the writer from the outside cylinder engines of the Caledonian Railway, of which the cylinders are placed beyond the direct influence of the heat in the smoke box, and considerably exposed to the atmosphere. Seventy-six were selected as average samples of diagrams obtained during the regular work of the engines. These have been analyzed in the way adopted for those of the Great Britain, and the mean results range from 9 per cent. deficiency, to as much as 67 per cent. excess at the greatest expansion. Specimens of the diagrams from No. 42, passenger engine, and from No. 125, goods engine, are given in fig. 2. These diagrams were taken by McNaught's Indicator, and the dotted lines show the actual curves which are affected by the oscillation, to which that indicator is subject at high velocities. The mean lines have been drawn on the diagrams on the principle which the writer has satisfied himself applies in the particular case of the indicator— that action and re-action are equal, and that therefore the mean line, or radical form, ought to inclose the same collective area of diagram as the fluctuations in the lines actually described, due partially to momentum, cutting off at one place as much as it incloses at another.

For the greater ratios of expansion, the final equivalent of the steam is much above the initial, and the greater the ratio the greater is the per centage of this excess, amounting to 67 per cent. with an expansion of 3 times. This relation is just what was found for the slow diagrams from No. 13, and there is no doubt the excess of steam, at the termination of the expansion, is due to the same cause, namely the condensation of the steam in the cylinder during admission, and during the first part of the expansion, and the subsequent re-evaporation of a portion of the precipitated steam. During the experiment, there was at all times ocular demonstration of the existence of water in the cylinder, in the spray which escaped from it through the indicator, and which was given off more abundantly the more expansively the steam was worked.

To find the general rate at which the per centage of condensation increases in these engines with the degree of expansion, the results obtained may be referred, as ordinates, to a base line representing the ratios of expansion. Let A B, fig. 4, be a base line divided to represent the total volumes by expansion in terms of the initial volumes; and from B draw the vertical scale to measure the relative per centages of condensation. From A set off on the base line the ratios of expansion, and for each ratio set off perpendicular distances by the vertical scale, equal to the respective percentages of the differences of water equivalents, col. 13, and define their extremities by points, setting off minus per centages below the line, and plus per centages above. The mean line CD, drawn through these points, is straight, and represents the mean rate at which the indicated condensation increases with the degree of expansion. It is found to meet the vertical from division 1, at 20 per cent. below, crosses the base line at a volume of 1.53, and terminates at E, the point due to an expanded volume of 3.4, and to a per centage of 70, and would, if produced, meet the vertical from B, at 924 per cent. The straightness of the line implies that the indicated per centage of condensation increases uniformly with the relative volume by expansion. For an expansion of 1.53 times, the per centage of condensation, or indicated difference of equivalents, is nothing; and, generally, for expansions advancing by half volumes, the per centages are as follows:

For every half volume of expansion there is an increase of 183 per cent. of indicated condensation, and this becomes so serious that for an expansion of four times, if this were practicable with ordinary valves and link motions, there would be 924 per cent. of loss by condensation, or a loss of nearly one-half of the total quantity of steam admitted.

For ready reference, it is expedient to find the relative expansion and indicated condensation for different periods of admission, yielded by ordinary link motions. The following table contains in col. 2 the total ex

pended volumes due by the nature of link motion to the several periods of admission in col. 1, and col. 3 contains the relative indicated per cent ages of condensation due to these expansions, measured from the diagram. Of the Indicated Condensation of Steam in Outside Cylinders during the Admission of Steam.

Though the losses shown in the 3d column are great, the real losses must be still greater; because the restoration of condensed steam, by which the losses have been measured, cannot be entire. The indications, indeed, fail to show any loss at all, at 50 per cent., as the re-evaporation balances the condensation during expansion. For 75 per cent., the re-evaporation (if any) is so slight as to leave a deficit of 12 per cent., by condensation, during expansion, compared with what was indicated as cut off. Now, the whole tenor of the evidence shows plainly that the degree of condensation increases as the admission is shortened; and it may be safely inferred that as 12 per cent. is shown to be lost in full gear, there is at least 12 per cent. of loss for 50 per cent. of admission, cutting off at half stroke. An approximate loss of 12 per cent. will, on this ground, be adapted for all admissions greater than half stroke; and 12 per cent. will also be added to the indicated losses for shorter admissions, as an approximation to the real conditions.

Col. 4 contains the approximate losses as thus revised, in parts of the indicated steam admitted. Adding the lost steam admitted to that indicated, the sum expresses the whole steam admitted and expanded; and col. 5 contains the per centage of approximate loss, expressed in terms of the whole steam so used, which is a more convenient form for reference. From this column it appears that for 40 per cent. admission, 17 per cent., or one-sixth of the steam, is condensed; for 30 per cent., one-fourth; for 20 per cent., one-third; and for 12 per cent., or mid gear, two-fifths, or not far from one-half.

It must be added that the foregoing deductions are based on steam pressures under 60 lbs., generally about 50 lbs., during admission. For higher pressures, and admissions above half stroke, the condensation is proportionally less, as will afterwards be shown.